0. Review Problems

0. Review Problems - Some Review Problems Here are some...

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Unformatted text preview: Some Review Problems Here are some differentiation and integration problems. You should also review your notes from the first two calculus courses. Please email me if you find any errors in the solutions. QUESTIONS 1. Find the derivative of f (x) = sin(x2 + x) + 2. 2. Find the derivative of f (x) = 2xesin x . 3. Find the derivative of f (x) = cos(tan x2 ). 4. Find the derivative of f (x) = 5. Find the derivative of f (x) = 2 x2 x+1 . x−1 x 1 + t3 dt. 1 + t3 dt. 2 6. Find the derivative of f (x) = π /2 7. Find 0 sin(x) dx. √ 3t4 + t2 + t t dt. t √ 3x2 x3 + 1 dx. xe−x dx. x3 sec2 (x4 + 1) dx. 1 dx. (x − 3)(x − 4) 8. Find 9. Find 10. Find 11. Find 12. Find 1 SOLUTIONS 1. f (x) = (2x + 1) cos(x2 + x). 2. f (x) = 2xesin(x) cos(x) + 2esin x . 3. f (x) = −2x sin(tan x2 ) sec2 x2 . 4. f (x) = −2 . (x − 1)2 5. f (x) = 1 + x3 . 6. f (x) = 2x(1 + x6 ). 7. 1. 8. (3/4)t4 + (1/2)t2 + (2/3)t3/2 + C . 9. (2/3)(1 + x3 )3/2 + C . 10. −xe−x − e−x + C . 11. (1/4) tan(x4 + 1) + C . 12. ln |x − 4| − ln |x − 3| + C . 2 ...
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0. Review Problems - Some Review Problems Here are some...

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