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Mathematics 143, Fall 1999, Final Exam


In problems 1 to 4, find the integrals:













5. Find the arc length of the curve y = 2x^3/2 from x = 0 to x = 3 by integration.


6. Find if each series is absolutely convergent, conditionally convergent, or divergent. State which test you use and show how it applies:










7. Let f(x) = ln(x) .

a) Write down the 4th Taylor polynomial T₄(x) for the function ln(x) expanding at "a" = 1 .

b) Estimate the value of ln(1.2) using part (a).

c) Find the estimate for the error in part (b) using Taylor’s Theorem.


8. Find the radius of convergence and the interval of convergence for the power series




9. Solve the differential equation






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