APCalculusMidtermReview.docVIP

AP Calculus: Midterm Review 2011-12 NAME ____________________ DATE __________ PER _____ Domain, Range, and Composite Functions EX 1] Find the domain of the function . EX 2] Find the range of the function . Composite Function: EX 3] Let and . Let Find . Find the domain of . Find the range of . EX 4] Find the domain of the function . Inverse Functions EX 1] Given , find . EX 2] Given , find . EX 3] Given , find if . Symmetry EX] Determine the symmetry for each of the following. Function Modifications: EX 1] Describe the relationship between . EX 2] Describe the graph of . Limits: EX 1] Find . EX 2] Find . EX 3] Find . EX 4] Find . EX 5] Find . EX 6] Find . EX 7] Find . EX 8] Find . Continuity EX 1] Determine any removable discontinuity of . EX 2] Let . Determine if f(x) is continuous at x = 2. Continuity and Differentiability EX 1] If is continuous at x = a, which of the following is NOT necessarily true? Why? is defined. b) exists. c) exists. d) . e) EX 2] Find an equation of the tangent line to the graph at the point (2,6). Use a TI-83 to graph the function and its tangent at the point. Confirm this answer with the derivative feature of the TI-83. Differentiation EX 1] If , what must be true? exists b) is continuous at . is defined at . d) none of these EX 2] If , find . EX 3] Which of the following is true for the function at ? Undefined Continuous, but NOT differentiable Differentiable, but NOT continuous Neither continuous nor differentiable Both continuous and differentiable EX 4] Let . Find . Chain Rule EX 1] Find y’ if . EX 2] Find if . The Product Rule EX 3] If , find . EX 4] Let . Find the slope of the tangent to at . The Quotient Rule EX 5] Find the derivative of . Implicit Differentiation EX 7] Find if . EX 8] Find if . Inte