# integral

1. (8 points) Evaluate cos(2 sin 2. (8 points) Given f(x) = r + sin I, find (F-1)(2). 3. Find the limits. (a) (8 points) lime; 10 tan-1 In (b) (8 points) lim .22 (c) (8 points) lim (7€ – c*). 100 4. Differentiate the functions. (a) (8 points) g(C)=ccosh = + ln(cosho); (b) (8 points) y = (2+)”. 5. (8 points) Strontium-90 has a half-life of 28 days. Suppose that we have a 16-mg sample of Strontium-90, after how many days will there be 1 mg remain? 6. Evaluate the Integrals. (a) (8 points) rcoshrdar; sin 2.r cos cdr; 12+1 dr. (b) (8 points) / sin (c) (8 points) / V7? 7. (8 points) Use Simpson’s rule with n = 1 to estimate the integral [” S. rኝdr. . sec 8. (8 points) Determine whether the improper integral dr is convergent. Find its value if it is. tan

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