01_Midterm1-Sample

01_Midterm1-Sample - to compute dy dx for y = p 3 x...

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University of California, Riverside Department of Mathematics Midterm 1 Mathematics 9A - First Year of Calculus Sample 1 Instructions: This exam has a total of 33 points. You have 50 minutes. You must show all your work to receive full credit You may use any result done in class. The points attached to each problem are indicated beside the problem. You are not allowed to use books, notes, or calculators. Answers should be written as p 2 as opposed to 1 : 4142135 ::: . 1. Find the following limits: (a) (3 Points) Find lim x ! 2 g ( x ) ; provided that lim x ! 2 h 4 g ( x ) x i = 5 : (see section 2.2) (b) (3 Points) Find lim x ! 0 sin(4 x ) 5 x : (see section 2.4) (c) (3 Points) Evaluate lim x 3 + x x 2 9 (see section 2.4) 2. (6 points) Consider the following graph of a function f : f ( x ) = 8 > > > > < > > > > : 1 x x < 1 2 1 ± x < 1 3 x = 1 x + 1 1 < x ± 2 1 x 2 2 < x 1
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-5 -4 -3 -2 -1 1 2 3 4 5 -2 -1 1 2 3 x y (a) Find lim x 1 f ( x ) (b) Find lim x 1 + f ( x ) : (c) Find lim x 1 f ( x ) : (d) Find lim x ! 1 f ( x ) : (e) Is f continuous at x = 1? 3. Let y = p 3 x 5 (a) (3 points) Use the
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Unformatted text preview: to compute dy dx for y = p 3 x &amp; 5 : (b) (3 points) Find the equation of the tangent line to y = p 3 x &amp; 5 at (2 ; 1) (see sections 2.7 and 3.1) 4. Find the derivatives of the following functions. Do not simplify. (a) (3 points) f ( x ) = (2 x &amp; 3) ( x 2 +5 x &amp; 2 ) x (see section 3.2, 3.4 and 3.5) (b) (3 points) g ( x ) = x 3 tan (sin (5 x 2 )) (see sections 3.2, 3.4 and 3.5) 2 5. At time t; the position of a body moving along the s &amp; axis is given by s = t 3 &amp; 6 t 2 + 9 t (in meters and seconds). (a) (2 points) Find the body&amp;s acceleration each time the velocity is : (b) (2 points) Find the body&amp;s speed each time the acceleration is : (c) (2 points) Find the total distance traveled by the body from time t = 0 seconds to t = 2 seconds. (see section 3.3) 3...
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01_Midterm1-Sample - to compute dy dx for y = p 3 x...

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