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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.6 - Problem 55ae
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.6 - Problem 55ae

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# Estimating error Refer to Theorem 7.2 and let f(x) = sin ISBN: 9780321570567 2

## Solution for problem 55AE Chapter 7.6

Calculus: Early Transcendentals | 1st Edition

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Problem 55AE

Estimating error  Refer to Theorem 7.2 and let $$f(x)=\sin e^{x}$$.

(a) Find a Trapezoid Rule approximation to $$\int_{0}^{1} \sin \left(e^{x}\right) d x$$ using n=40 subintervals.

(b) Calculate $$f^{\prime \prime}(x)$$.

(c) Explain why $$\left|f^{\prime \prime}(x)\right|<6$$ on [0,1], given that e<3. (Hint: Graph $$f^{\prime \prime}$$.)

(d) Find an upper bound on the absolute error in the estimate found in part (a) using Theorem 7.2.

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Chapter 13:  The ABC of Prejudice involves three components: o Affective Component (emotional component), referred to as prejudice o Behavioral Component (actions), referred to as discrimination o Cognitive Component (thinking). referred to as stereotyping  Prejudice is an emotional reaction to a group, hostile or negative attitude toward people in a distinguishable group, based solely on their membership in that group  The behavioral component is the unjustified negative or harmful action toward members of a group simply because of their membership in that group  The cognitive component is a generalization about a group of people in which identical characteristics are assigned to virtually all members of the group, regardless of actual variation among the members  We can measure prejudice two ways: o Explicit Measures: involve directly (explicitly) asking people about their beliefs (self­report measures) o Implicit Measures: involve finding an indirect way to measure people’s beliefs (e.g., implicit association test; IAT)  The Ultimate Attribution Error (UAE) people attribute a group’s behavior to internal factors and overlook situational explanations  The Social Identity Theory is when people strive to enhance their self­esteem partly through their social identities: o In­group: group we belong to o Out­group: group we do not belong to  Relative Conflict Theory

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