mid1_short (1)

mid1_short (1) - MIDTERM 1 FOR MATH 151 October 6 2010 NAME...

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MIDTERM 1 FOR MATH 151 October 6, 2010 NAME . ................................................................. SECTION . ....................... Do all problems, in any order. Show your work. An answer alone may not receive full credit. No texts, notes, or calculators. A formula sheet is attached. (15) Problem 1. Compute the following limits. Supporting work for each answer must be given to earn full credit. L’Hospital’s rule is not allowed. (5) (a) lim x 3 4 - 5 x + 1 6 - 2 x (5) (b) lim x 0 1 - sec x x 2 (5) (c) lim x 2 - | x - 2 | x 2 - 4 (10) Problem 2. The function f is deﬁned as follows: f ( x ) = ax + b if x < 1 2 if x = 1 b x - cx + x 2 if x > 1 where a,b and c are constants. (5) (a) Find all a,b,c such that f is continuous. (5) (b) Find all a,b,c such that f is diﬀerentiable.

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(10) Problem 3. Let f ( x ) = x 2 x 6 + 1 . Give a careful evidence, including speciﬁc assertions or theorems, that the equation: f ( x ) = π 10 (5) (a) has at least 2 solutions. (5) (b) has at least 4 solutions.
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mid1_short (1) - MIDTERM 1 FOR MATH 151 October 6 2010 NAME...

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