M408C - rev1prob

# M408C - rev1prob - y = x sin(2 x 1 7 Find the equation of...

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M408C Calculus 55815/20/25 Fall 2002 Midterm 1 Review Problems The exam will cover the following sections of Salas and Hille’s Calculus , 8th edition: 2.1, 2.3–2.5, 3.1–3.3, 3.5–3.7, 4.1–4.2. 1. Decide whether or not the indicated limit exists. Evaluate the limits that do exist. (a) lim x 1 x 2 - 2 x + 1 x 2 - 1 (b) lim x 2 + f ( x ) if f ( x ) = ± 2 x - 1 , x 2 x 2 - x, x > 2 . 2. Evaluate the limits (a) lim x 0 7 x 2 sin 2 5 x (b) lim x 0 tan 3 x x 2 + 4 x 3. (a) Find f 0 ( c ), if it exists f ( x ) = ± 3 x 2 , x 1 2 x 3 + 1 , x > 1; c = 1 (b) Is it true that f ( x ) = | 2 x - 5 | is diﬀerentiable everywhere? 4. (a) Find the derivative of the function f ( x ) = ( x 2 + 1) 2 ( x - 1) 3 (b) Evaluate dy/dx at x = 2 for y = x 2 - 3 x + 1 x + 2 5. Find dy/dt for y = 1 + u 1 - u , u = t 2 / 3 6. Find the second derivative of

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Unformatted text preview: y = x sin(2 x + 1) 7. Find the equation of the tanget line to the curve y = cos 2 x at x = π/ 4. 8. Find equations for tangent and normal lines at the indicated point by using implicit diﬀerentiation 2 x 2 + 2 xy + y 2 = 2; (1 ,-2) M408C Calculus 55815/20/25 Fall 2002 9. Find the intervals on which f increases and intervals on which f decreases f ( x ) = x-1 x + 1 10. Is it true that the function f ( x ) = ± x 3 , x <-1 2 x + 2 , x ≥ -1; increases on all of (-∞ , ∞ )? Explain your reasoning....
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## This note was uploaded on 06/19/2008 for the course M 408 C taught by Professor Treisman during the Fall '07 term at University of Texas.

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M408C - rev1prob - y = x sin(2 x 1 7 Find the equation of...

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