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.
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