05_Midterm1-Sample

05_Midterm1-Sample - p & 2 x + 5 : (b) (3...

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University of California, Riverside Department of Mathematics Midterm 1 Mathematics 9A - First Year of Calculus Sample 5 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) If lim x ! 3 h f ( x ) 2 x + 1 i = 2 ; lim x ! 3 f ( x ) : (see section 2.2) (b) (3 Points) Find lim x ! 0 tan(4 x ) sin(6 x ) : (see section 2.4) (c) (3 Points) Evaluate lim x !1 2 x 3 2 x +3 3 x 3 +3 x 2 3 (see section 2.4) 2. (6 points) Let f ( x ) = 2 x + 5 : Prove that lim x ! 3 f ( x ) = 11 by showing that for each " > 0 there is a number & > 0 so that j f ( x ) 11 j < " for all x with j x 3 j . 3. Let y = 3 p 2 x + 5 (a) (3 points) Use the to compute dy dx for y = 3
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Unformatted text preview: p &amp; 2 x + 5 : (b) (3 points) Find the equation of the tangent line to y = 3 p &amp; 2 x + 5 at ( &amp; 2 ; 9) (see sections 2.7 and 3.1) 4. Find the derivatives of the following functions. Do not simplify. (a) (3 points) f ( x ) = (3 x &amp; 5) ( &amp; x &amp; 2 +4 x ) sec( &amp; 2 &amp; 2 x ) (see section 3.2, 3.4 and 3.5) 1 (b) (3 points) g ( x ) = csc &amp; tan &amp; 1 x &amp; 2 x 2 (see sections 3.2, 3.4 and 3.5) 5. A rock thrown vertically upward from the surface of moon at a velocity of 24 m/sec reaches a height of s ( t ) = 24 t &amp; : 8 t 2 m in t seconds (a) (2 points) Find the rock&amp;s velocity and acceleration as a function of t: (b) (2 points) How long does it take the rock to reach its&amp;s highest point? (c) (2 points) How high does the rock go? (see section 3.3) 2...
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05_Midterm1-Sample - p &amp;amp;amp; 2 x + 5 : (b) (3...

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