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Unformatted text preview: MATH 217: MIDTERM2 (SPRING 2007.) N ame:_____________________________ Section: ____ _____ TA:________________ Score:
Problem 1.______r_____________l____
Problem 2 ____________________________
Problem 3 ____________________________ Problem 4.n____________._____T__
Problem 5 ____________________________ Problem 6 Total:____r _____________________ Instruction: Show all work. No work = no credit, even if you have a
correct answer. References and calculator are not allowed. ‘ Problem 1 (10 points): Find the volume of the solid generated by. revolving
the region between the xaxis and the curve 3/ =_%, 1 S a: S 4, about the .
xaxis. " V 20:4 Problem 2 (10 points): The function f(a:) = 3953;; is deﬁned on {0,+oo).
Show that f is one to one. Then ﬁnd the expression of its inverse function.
(You don’t have to specify the domain and range of its inverse function). Problem 3 (10 points): Use logarithm differentiation to compute f’ (x),
where f(:z:) = (2x + 1F” , cc > —%. Then evaluate f’(0). , Problem 4 (20 points): Compute the following:
(a) % Ink953%) . Problem 5 (10 points): (a) Show that any two logarithm functions logaa:
and logbx (here a, b > 1) have the same growth rate as a: ——> +00. (b) Show that :02 + sinx is of smaller order than 2x as cc —> +00, in other
words, 3:2 + sinac = 0(2‘”). Problem 6 (10 points) Evaluate the following:
(a) tan(sin‘1(%)) ' (b) cos—1(cos(——§—)) ...
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 Fall '08
 GOMEZ
 Algebra

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