math 2b midterm

# math 2b midterm - x 2 14 Find the derivative of the...

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1 . Compute 4 x dx 2 . Compute sec 2 (3 x ) dx 3 . Compute x + x x dx 4 . Compute e - 3 x dx 1

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5 . Find f ( x ) for the function f ( x ) = sin x - 2 1 - t 2 dt 6 . Compute y for the function y = e 3 x ln x 7 . Compute y for the function y = x ln x 2
8 . Let R be the region bounded by y = e - x , 0 x 1 , and y = 0 . Find the area of R . 9 . Let R be the region bounded by y = - x , y = x 2 , and 0 x 2 . Find the area of R . 3

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10 . . Find the arc length of y = 2 x 3 / 2 , 0 x 7 . 11 . Let R be the region bounded by y = x 2 and y = 1 . Compute the volume of the solid formed by revolving R about the line y = - 2 . 4
12 . Let f ( x ) = x 3 + 2 x + 1 . Assume f has an inverse and compute d dx f - 1 ( a ) , where a = 1 . 13 . Find the derivative of the function

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Unformatted text preview: x 2 )) . 14 . Find the derivative of the function y = e cot x . 15 . Compute ± e cot x sin 2 x dx 5 16 . Compute ± e x √ 1-e x dx 17 . Compute ± e 2 x-1 e x dx 18 . Compute ± (1+ln x ) 2 x dx 19 . Compute ± 1 x + x ln x dx 6 20 . Compute ± sec(1 /x ) x 2 dx 21 . Compute ± cos( √ x ) √ x dx 22 . Compute ± sin(ln x ) x dx 23 . Compute ± sec 2 x tan 2 xdx 7 24 . Compute ± 1 √ xe √ x dx 25 . Compute ± ( x-1 /x ) 2 dx 8...
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