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Solved: 5964. Derivatives Consider the following parametric curves. a. Determine dy>dx

Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321947345 | Authors: William L. Briggs ISBN: 9780321947345 167

Solution for problem 61 Chapter 10.1

Calculus: Early Transcendentals | 2nd Edition

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Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321947345 | Authors: William L. Briggs

Calculus: Early Transcendentals | 2nd Edition

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Problem 61

5964. Derivatives Consider the following parametric curves. a. Determine dy>dx in terms of t and evaluate it at the given value of t. b. Make a sketch of the curve showing the tangent line at the point corresponding to the given value of t. x = cos t, y = 8 sin t; t = p>2 6

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Psychology Exam #3 Study Guide- Professor Cate’s Class Highlight = Important People Highlight = Important Idea Highlight = Key Term CHAPTER 7: LEARNING  Topics in this Chapter:  Classical conditioning  Operant conditioning  Biological and cognitive components of learning  Observational learning  Learning: the process of acquiring new and relatively enduring info or behaviors.  How does learning happen other than through language/words  We learn from experience:  When we learn to predict events we already like or don’t like by noticing other events or sensations that happen first.  When our actions have consequences.  When we watch what other people do.  We learn by association:  When two stimuli (events or sensations) tend to occur together or in sequence.  When actions become associated with pleasant or aversive results.  When two pieces of info are linked.  Associative and Cognitive Learning  Classical conditioning: learning to link two stimuli in a way that helps us anticipate an event to which we have a reaction.  Operant conditioning: changing behavior choices in response to consequences.  Cognitive learning: acquiring new behaviors and info through observation and information, rather than by direct experience.  Operant and Classical Conditioning are different forms of Associative Learning  Classical conditioning: involves respondent behavior, reflexive, automatic reactions such as fear or craving.  These reactions to unconditioned stimuli (US) become associated with neutral (then conditioned) stimuli.  The experimental (neutral) stimulus repeatedly precedes the respondent behavior, and eventually triggers that behavior.  Sign Tracking: want to hang out with the things you like (ex: when you’re bored, you would immediately go to the fridge to search for food.)  Operant conditioning: involves operant behavior, chosen behaviors which “operate” on the environment.  These behaviors become associated with consequences which punish (decrease) or reinforce (increase) the operant behavior.  The experimental (consequence) stimulus repeatedly follows the operant behavior, and eventually punishes or reinforces that behavior.  Cognitive Learning  Cognitive learning refers to acquiring new behaviors and info mentally, rather than by direct experience. This occurs by:  observing events and the behavior of others.  using language to acquire info about events experienced by others.  Ivan Pavlov’s Discovery  While studying salivation in dogs, Ivan Pavlov found that salivation from eating food was eventually triggered by what should have been neutral stimuli such as:  Just seeing the food  Seeing the dish  Seeing the person who brought the food  Just hearing that person’s footsteps  Before conditioning:  Neutral Stimulus (NS): a stimulus which doesn’t trigger a response (ex: NS-a bell)  Unconditioned stimulus (US) and response (UR): a stimulus which triggers a response naturally, before/without any conditioning (ex: US- delicious dog food UR- dog salivates)  During conditioning:  The bell/tone (NS) is repeatedly presented with the food (US) (ex: bell+ food= dog salivates)  After conditioning:  The dog begins to salivate upon hearing the tone (neutral stimulus becomes conditioned stimulus). (ex: Conditioned (formerly neutral) stimulus Conditioned response: dog salivates)  Conclusion: The UR and the CR are the same response, triggered by different events.  The difference whether conditioning was necessary for the response to happen.  Conclusion: The NS and the CS are the same stimulus.  The difference is whether the stimulus triggers the conditioned response.  Ivan Pavlov’s Legacy:  Insights about conditioning in general:  It occurs in all creatures.  It is related to biological drives and responses.  Insights about science:  Learning can be studied objectively, by quantifying actions and isolating elements of behavior.  Insights from specific applications:  Substance abuse involves conditioned triggers, and these triggers (certain places, events) can be avoided or associated with new responses.  John B. Watson and Classical Conditioning: Playing with Fear  9 month old Little Albert was not afraid of rats.  John B. Watson and Rosalie Rayner then clanged a steel bar every time a rat was presented to Albert.  Albert acquired a fear of rats, and generalized this fear to other soft and furry things.  Watson Prided himself in his ability to shape people’s emotions. He later went into advertising.  Operant Conditioning  Operant conditioning involves adjusting to the consequences of our behaviors.  Examples:  We may smile more at work after this repeatedly gets us bigger tips.  We learn how to ride a bike suing the strategies that don’t make us crash.  How it works:  An act of chosen behavior (a “response”) is followed by a reward or punitive feedback from the environment.  Results:  Reinforced: behavior is more likely to be tried again.  Punished: behavior is less likely to be chosen in the future.  Response: balancing a ball Consequence: receiving food Behavior is strengthened  Thorndike’s Law of Effect  Edward Thorndike- Thorndike’s law of effect: behaviors followed by favorable consequences become more likely, and behaviors followed by unfavorable consequences become less likely.  B.F. Skinner: Behavioral Control  B.F. Skinner:  Skinner envisioned societies where desired behaviors were deliberately shaped with reinforcement.  How can we more carefully measure the effect of consequences on chose behavior  What else can creatures be taught to do by controlling consequences  What happens when we change the timing of reinforcement  Reinforcement:  Reinforcement: feedback from the environment that makes a behavior more likely to be done again.  Positive + reinforcement: the reward is ADDING something desirable.  Negative – reinforcement: the reward ENDING something unpleasant.  Shaping Behavior:  Shaping: guiding a creature toward the behavior by reward behavior that comes closer and closer to the desired behavior.  Example: Seal is rewarded with fish whenever it balances a ball on their nose for a long time.  Operant Effect: Punishment  Punishments have the opposite effects of reinforcement. These consequences make the target behavior less likely to occur in the future.  Positive + punishment: You ADD something unpleasant/aversive (ex: spank the child)  Negative – punishment: You TAKE AWAY something pleasant/desired (ex: no TV)  When is punishment effective  Works best in natural settings when we encounter punishing consequences from actions (ex: reaching into fire).  Operant conditioning helps us to avoid dangers.  Less effective when we try to artificially create punishing consequences for other’s choices  Severity of punishments is not as helpful as making the punishments immediate (signs showing your speed) and certain.  Summary: Types of Consequences  Adding stimuli  Subtract stimuli  Outcome  Positive +  Negative –  Strengthens target Reinforcement Reinforcement behavior  (You get candy)  (I stop yelling)  (You do chores)  Positive +  Negative –  Reduces target Punishment Punishment behavior  (You get spanked)  (No cell phone)  (cursing) CHAPTER 10: MOTIVATION AND EMOTION  Motivation: a need or desire that energizes behaviors and directs it towards a goal.  Perspectives on Motivation  Instinct Theory Evolutionary Perspective  Drive-Reduction Theory  Arousal (Optimization) Theory  Hierarchy of Needs/Motives  Different ways of thinking and the way motivation works  relate to “push” of biological processes and the “pull of culture, social forces, and ideals.  Do instincts direct human behavior  Instinct: a fixed (rigid and predictable) pattern of behavior that is not acquired by learning and is likely to be rooted in genes and the body. (ex: nesting behavior)  Drive Reduction:  A drive is an aroused/tense state related to a physical need such as hunger or thirst.  Drive-reduction theory refers to the idea that humans are motivated to reduce these drives, such as eating to reduce the feeling of hunger. This restores homeostasis, a steady internal state.  Need (food, water) Drive (hunger, thirst) Drive-reducing behaviors (eating, drinking)  Seeking Optimum Arousal:  Curiosity, as with kids and these monkeys, may seek stimulation to reach an optimum arousal level.  Curiosity can be a basic need or drive to get to know one’s environment to improve the chances of survival.  A hunger for stimulation, novelty…  Performance and Arousal Level:  What happen when we succeed at raising our arousal levels  Yerkes-Dodson Law: Arousal levels can help performance but too much arousal can interfere with performance. (ex: taking the exam-moderate arousal is best)  The effect of arousal on performance depend on how comfortable we are with the task.  Hierarchy of Needs/Motives:  Abraham Maslow proposed that humans strive to ensure that basic needs are satisfied; then, they find motivation to pursue goals that are higher on this hierarchy.  Another Motivation: “To Belong”  What do people need besides food and sex  Aristotle: social life  Alfred Adler: community  Wretched means to ‘be without kin nearby’  Roy Baumeister, Mark Leary, and Abraham Maslow say we need: “TO BELONG”  Belonging: being connected to others, part of a group or family or community.  Why do we need to belong  Evolutionary psychology perspective: seeking bonds with other aids survival in many ways.  Keeping children close to caregivers  Mutual protection in a group  Cooperation in hunting and sharing food  Division of labor to allow growing food  Emotional support to get through crises  Balancing Bonding with Other Needs:  The need to bond with others is so strong that we can feel lost without close relationships.  However, we also seem to need autonomy and a sense of personal competence/efficacy.  There is a tension between “me” and “us”, but these goals can work together.  belonging builds self-esteem, and prepares us for confident autonomy.  Need to Belong Leads to:  Loyal to friends, teams, groups, and families.  However, the need to belong also leads to:  Changing our appearance to win acceptance.  Staying in abusive relationships.  undermine our autonomy and our sense of self- efficacy/competence. (less likely to leave an abusive relationship)  Joining gangs, nationalist groups, and violent organizations.  Social Networking = Social connection  Do updates and tweets build connection  Use of social networking can become a compulsion, sacrificing face-to-face interaction and in-depth conversation.  Research shows: Portrayal of one’s self online is often close to one’s actual sense of self.  Research shows: Online social networking is associated with  Narcissism/self-centeredness  Less connection to neighbors  More connection to people who share our narrow interests and viewpoints.  Motivation to excel in work:  Achievement motivation, a desire for:  Accomplishment of goals  Mastery of skills  Meeting of standards, control of resources  What helps us satisfy our achievement motivation  Discipline: Sticking to task despite distractions  10-year rule: Having enough experience to develop expertise in a field  Grit: passionate persistence at a goal  Hardiness: resilience under stress  Introduction to Emotion  Physiological Arousal:  Comes before emotion (James-Lange theory)  Comes with emotion (Cannon-Bard theory)  Becomes an emotion when cognitive appraisal/label is added (Schacter-Singer two-factor theory)  Emotions and the brain: sometimes cognition is bypassed in emotional reactions  Emotions and the body: The Autonomic Nervous system  Emotions with different brain and body response patterns  Emotion: Arousal, Behavior, and Cognition  Someone cuts you off on the road. You may feel the emotion of anger. Emotions are a mix of:  Expressive behavior: yelling, accelerating  Bodily arousal: sweat, bounding heart  Conscious experience: (thoughts, especially the labeling of the emotion) “What a bad driver! “I am angry, even scared” “better calm down.”  An emotion is a full body/mind/behavior response to a situation.  Emotion and mood is not the same thing. Mood is NOT a response to a situation, and an attitude, which is a predisposition to act in a certain way in a situation. Differentiates an emotion from one’s affect, which are the outwardly expressive signs, especially facial expression and other nonverbal behaviors, that seems to be related to emotions.  Is Experienced Emotion as Universal as Expressed Emotion  Carroll Izzard suggested that there are ten basic emotions: those evident at birth plus contempt, shame, and guilt.  Joy (mouth forming smile, cheeks lifted, twinkle in eye)  Anger (brows drawn together and downward, eyes fixed, mouth squarish)  Interest (brows raised or knitted, mouth softly rounded, lips may be pursed)  Disgust (nose wrinkled, upper lip raised, tongue pushed outwards)  Surprise (brows raised, eye widened, mouth rounded in oval shape)  Sadness (brow’s inner corner raised, mouth corners drawn down)  Fear (brows level, drawn in and up, eyelids lifted, mouth corners retracted)  Embodied Emotion: The role of the autonomic nervous system  The physiological arousal felt during various emotions is orchestrated by the sympathetic nervous system (arousing), which triggers activity and changes in various organs.  Later, the parasympathetic division (calming) calms down the body.  Embodied Emotion: How Do Emotions Differ in Body Signs  It is difficult to see differences in emotions from tracking heart rate, breathing and perspiration.  There is also a large overlap in the patterns of brain activity across emotions.  There are some small differences; for example, fear triggers more amygdala activity than anger.  A general brain pattern: hemispheric difference  Positive “approach” emotions (joy, love, goal-seeking) correlate with left frontal lobe activity (good for analyzing details).  Negative “withdrawal” emotions (disgust, fear, anger, depression) correlate with right hemisphere activity (good for understanding the big picture).  Expressed and Experienced Emotion:  Detecting emotions in others  Gender, emotion, nonverbal behavior  Culture and expressed emotions  Using context to read emotions  Are there universally recognized emotion  Do facial expressions affect feelings  Detecting Emotions in Others  People read a great deal of emotional content in the eyes (“the window to the soul”) and the faces.  Introverts are better at detecting emotions; extroverts have emotions that are easier to read.  We are primed to quickly detect negative emotion words.  Those who have been abused are biased toward seeing fearful faces as angry.  Detecting Lies and Fakes:  Polygraph (detecting physiological arousal) fail sometimes at correctly identifying when people are lying.  Visible signs of lying: eye blinks decrease, and other facial movements change.  Gender and Emotional Expression and Detection:  Women seem to have greater and more complex emotional expression.  Women are also more skilled at detecting emotions in others.  People tend to attribute women’s emotionality to their dispositions, and attribute men’s emotions to their circumstances.  Culture and Emotional Expression: Are There Universally Recognized Emotions  There seem to be some universally understood facial expressions.  People of various cultures agree on the emotional labels for the expressions on the face.  People in other studies did have ore accuracy judging emotions from their own culture.  Emotion Detection and Context Cues:  Faces are exactly the same but the emotion changes based on context: the situation, gestures, and the tears.  Linking Emotions and Expressive Behaviors: Facial Feedback:  The facial feedback effect: facial position and muscle changes can alter which emotion we feel.  Examples:  In one study, people whose faces were moved into smiling or frowning positions experienced a change in mood.  Extending a middle finger or thumb while reading led to seeing characters with hostility or positive attitude.

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Textbook: Calculus: Early Transcendentals
Edition: 2
Author: William L. Briggs
ISBN: 9780321947345

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Solved: 5964. Derivatives Consider the following parametric curves. a. Determine dy>dx