# Exam I - sec b dx x x x âˆ 4 2 2 2 1 c âˆ dx x x ln d âˆ dx...

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Mathematics 3B Honors – Castroconde Name: Exam I (Chapters 7 and 8) I.D.#: Page 1 2 3 4 5 6 Total Points TO GET FULL CREDIT, SHOW ALL YOUR WORK. 1. First use Calculus to show that the function 3 2 ) ( 3 + = x x f is one-to-one. Then find a formula for its inverse function. 2. Find ) 2 ( 1 - f dx d if x x x x f 2 ) ( 3 5 + - = . 3. Sketch the graph of each function. Label intercepts, asymptotes (if any), etc. a. 2 ) ( 1 + = - x e x f b. 1 ) 2 ln( ) ( - + = x x f

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4. Find the exact value of each expression. a. 2 ln 5 e b. ( 29 32 1 2 2 log ) 8 ( log + c. ) 1 cosh( - d. ( 29 ( 29 2 1 arcsin tan - 5. Solve each equation. a. 1 ) 1 ln( ) 1 ln( = - + + x x b. 2 . 0 ) sin( = x 6. Find the derivative of each function. a. 2 ) 5 ln( ) ( x x x f = b. ) 3 arctan( 5 ) ( 2 x x f x = c. ) cosh( ) ( ) cosh( x x e e x f + =
7. If ) arctan( y x y + = , find dx dy . 8. Evaluate each limit. a. ) sin( lim x e x x - b. x x x x + - 2 0 ) cos( 1 lim 9. Evaluate each integral. a. + dx x x x ) sec( 5 ) tan(

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Unformatted text preview: ) sec( b. dx x x x âˆ«-+ 4 2 2 2 1 c. âˆ« dx x x ) ln( d. âˆ« dx x ) 4 ( sin 2 e. âˆ« + dx x x 2 1 1 10. Find the partial fraction decomposition of x x x +-3 1 . 11. How large should we take n in order to guarantee that the Midpoint Rule approximation of âˆ« 2 1 1 dx x is accurate to within 0.0001? 12. Evaluate each integral. a. âˆ«-3 1 1 x dx . b. dx x âˆ« âˆž + 1 3 ) 1 2 ( 1 13. Use the Comparison Test to determine whether dx x e x âˆ« âˆž-+ 1 2 is convergent or divergent. 14. Find the area of the region in the first quadrant bounded by the coordinate axes and x e y-= ....
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Exam I - sec b dx x x x âˆ 4 2 2 2 1 c âˆ dx x x ln d âˆ dx...

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