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1007Test2_09

# 1007Test2_09 - 1 3 3 3 2 3 a For what value of c the...

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Test 2, Wednesday February 11, 2009 MATH 1007G Last Name :_________________ First Name:_______________ ID #:____________________ Total marks:36 Total time: 50 minutes No Calculators are allowed. Show your work. Question 1. Find the following limits, if they exist. If the limit does not exist, determine whether it is , - ∞ or neither. a) [3.5] lim x x x x x - + - 1 3 2 2 1 b) [3.5] lim x x x x → -∞ - - - 1 2 3 2 2 c) [3.5] lim x x x + - 0 1 1 d) [3.5] lim [ln( ) ln( )] x x x → ∞ + - 2 2 1 2 e) [2] lim x x x - - 0 1 1 Question 2. [2] Fill in the blanks (No explanation is required here) a) lim arccos ............... x x - = 1 b) lim ln ......................... x x + = 0 Question 3. [3] Show that lim cos x x x = 0 2 2 0

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Test 2, Wednesday February 11, 2009 MATH 1007G Question 4. [4] Find the horizontal asymptote(s) and vertical asymptote(s) of the curve f x x x ( ) = - - 2 4 2 3 Question 5. [3] Let f x x x x if x c if x ( ) ( )( ) = - - + =
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Unformatted text preview: 1 3 3 3 2 3 . a) For what value of c , the function is continuous at x = 3 ? b) Let c = 5 . Is the function differentiable at x = 3 ? Why? Question 6. [2] The given limit lim x x x x → + --1 4 2 1 represents the derivative of a function f at a point a . State a function f and a . Hint: The difference quotient is expressed in the form: f x f a x a ( ) ( )--Question 7. Consider the function f(x) given by f x x x if x x if x ( ) = +-< + ≥ 1 3 3 2 3 a) [1] If t < 1 , then f t ( ) ............ 4-= . (Give the answer only) b) [4] Find the limits lim ( ) x f x → + 3 and lim ( ) x f x →-3 . If a limit does not exist, determine whether it is + ∞ ,- ∞ or neither. c) [1] Is the function continuous at x = -2 ?...
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1007Test2_09 - 1 3 3 3 2 3 a For what value of c the...

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