M408C - Review 2

M408C - Review 2 - 2 x ² dx 6 Find f from the information...

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M408C Calculus 55815/20/25 Fall 2002 Midterm 2 Review Problems The exam will cover the following sections of Salas and Hille’s Calculus , 8th edition: 4.3–4.8, 5.1–5.7, 6.1 1. Find the critical numbers and classify the extreme values (a) f ( x ) = x p 4 - x 2 (b) f ( x ) = tan x - 2 x, - π 3 x < π 2 2. Find the intervals of convexity and concavity and the points of inﬂection (if any) (a) f ( x ) = 2 x 2 - 5 x + 2 (b) f ( x ) = 2 x x 2 + 1 3. Find the vertical and horizontal asymptotes of f ( x ) = 2 x x 2 - 1 . 4. Given that R 1 0 f ( x ) dx = 5, R 3 0 f ( x ) dx = 3, R 7 3 f ( x ) dx = 1 ﬁnd each of the following: a. R 7 0 f ( x ) dx b. R 3 1 f ( x ) dx c. R 7 1 f ( x ) dx d. R 0 3 f ( x ) dx 5. Evaluate the deﬁnite integral (a) Z 4 1 ( x 3 / 2 - x 1 / 2 ) dx (b) Z π/ 3 0 ± 2 π x - 2 sec

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Unformatted text preview: 2 x ² dx 6. Find f from the information given f 00 ( x ) = 6 x-2 , f (0) = 1 , f (0) = 2 . 7. Evaluate the integral by a u-substitution (a) Z x-3 / 4 ( x 1 / 4 + 1)-2 dx (b) Z 3 r √ r 2 + 16 dr M408C Calculus 55815/20/25 Fall 2002 8. Calculate the derivative d dx Z 1+ x 2 dt √ 2 t + 5 ! 9. Find the area between the graph of f and the x-axis f ( x ) = x 2-4 , x ∈ [1 , 2] . 10. Sketch the region bounded by the curves and ﬁnd its area x + y = 2 y 2 , y = x 3 ....
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M408C - Review 2 - 2 x ² dx 6 Find f from the information...

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