Final Part 2

# Final Part 2 - (f) the intervals where the function is...

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MA 141-002 Final Exam December 13, 2006 Part 2 To receive full credit on each question, you must show all work! Absolutely no calculators are allowed on this part of the exam!! 1. Find the derivative of xe y + 1 = xy . 2. Find an equation of the line tangent to the curve y = 1 - x 1+ x at x = 2. 3. Find dy dx of y = x sin x using logarithmic diﬀerentiation. 4. For g ( x ) = x 1 3 ( x + 4) ﬁnd the following: (a) the domain (b) the zeros (c) the y-intercept (d) the intervals where the function is increasing and/or decreasing (e) the coordinates of the local maxima and/or minima

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Unformatted text preview: (f) the intervals where the function is concave up and/or down (g) the coordinates of the inﬂection points (h) the sketch 5. Find the limit. lim x →∞ e 3 x x 2 6. Evaluate the integral: Z cos( √ x ) √ x dx 7. Evaluate the integral: Z x ln( x ) dx 8. Evaluate the integral: Z sin 3 (3 x )cos(3 x ) dx 9. Evaluate Z dx x 3-x 10. Evaluate Z 4 x 3-x x 4 + 10 x 2 + 25 dx Extra Credit: Evaluate the integral: Z √ 4-x 2 dx (Hint: Use trig substitution)...
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## This note was uploaded on 11/27/2008 for the course MA Calculus I taught by Professor Abernathy during the Fall '08 term at N.C. State.

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Final Part 2 - (f) the intervals where the function is...

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