Calculus I Exam III, Fall 2007: Part I and II, Exams of Calculus

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Name: Calculus I; Fall 2007, Exam III

Part I

Part I consists of 6 questions, each worth 7 points. Clearly show your work for each of the problems listed. Find y′^ if: (1) y = x tan−^1 (x)

(2) y = (^) ln(xx)

(3) y = x^2 ex 3

1

(4) y = ln(sin(x))

(5) Evaluate the limit

lim x→ 5

cos(x) x^2 + 1

(6) Evaluate the limit

lim x→∞

ex^ + x e^2 x

(3) Find y′^ if y = (sin(x))

(^3) (x) 5 (7x+8)^9

(4) Simplify y = cos(tan−^1 (x)), then find y′.

(5) Use a linear approximation of the function y = f (x) =

x at an appropriate point x = a to estimate the value of