Calculus 1 Final Exam - Math 221 Fall, 2010

1.	Evaluate each of the following limits. Any correct method may be used. a. lim ( x / ln (x – 1 ) b. lim 1 / ( x – 2) x →4 x → 2- c. lim √( x + 1 ) / (x^2 + 4 ) d. lim (1 + 3x)^2/x x →∞ x → 0+ Answers: a. 4/ln3 b. - ∞ c. 0 d. e^6
2.	Evaluate each derivative. Use any (correct) method. a. d/dx (x ln x) b. d/dx (cos x / x)^1/4 c. Find dy/dx ex = x exp(y^2) Answers: a. 1 + ln x b. – sin x / (4x^1/4 cos^3/4x - cos^1/4x / (4 x^5/4) c. dy/dx = [ ( x – 1) / x ] [ 1 / 2( x – ln x)^1/2 ]
3.	Evaluate each definite or indefinite integral. e^4 a. ∫ 1 / √( 1 – x^2 ) b. ∫ (3x – 2)^20 dx c. ∫ 1 / ( x √ ln x ) e Answers: a. sin^-1(x) + C b. (1/63) (3x – 2)^21 + C c. 2
4.	A particle is moved along the x-axis by a force that measures 2(2+x)^-2 pounds x feet from the origin. Find the work done in moving the particle from x=1 to x=4. Answer: 1/3
5.	Find the average value of f(x) = x^3 – 1 on the interval [ -1, 2 ]. Answer: 1/4 Click here to continue with this exam.

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