sofferprobs1

# sofferprobs1 - Review Problems for the rst exam in Math 135...

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Review Problems for the first exam in Math 135 Spring 2009. NOTE : These are only practice problems! The exam will cover all the material through section 3.5. 1. Find the equation of the line that passes through (2 , 4) and is perpendicular to the line 2 x + 3 y = 12. 2. Let f ( x ) = p x 2 + 2 x - 15 , g ( x ) = 1 x a) Find the domain of the function f ( x ). b) Find g ( f ( x )) and f ( g ( x )). c) Find the domains of g ( f ( x )) . 3. Find the exact value of each of the following limits. Show all work and/or give reasons for your answers: a) lim x 2 x 2 - 5 x + 6 x 2 - 4 b) lim x 4 x 2 - 5 x + 6 x 2 - 4 c) lim x 0 tan 2 x tan 7 x d) lim x 0 3 + x - 3 x e) lim x 3 | x - 3 | x - 3 f) lim x 0 1 - cos x x 2 4. Let g ( x ) = x 5 + x 3 +30. Without graphing the function g , use a theorem to show that there is at least one number c ( - 2 , 2) such that g ( c ) = 0. HINT: don’t try to find c ! 5. Let f ( x ) = x 2 + 1 x > 2 A x = 2 2 x + 1 2 > x 0 x 2 + 3 x < 0 a)For what value of A is f continuous at x = 2? Explain!

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