Math 272
Group Quiz
Name
Directions: Show your work for each exercise neatly and completely.
1. Suppose f(x) = cos x.
a) Write the Taylor series expansion of f about a = 0 to see the pattern of the terms.
b) Find the interval of convergence for the Taylor Series of f.
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c) Estimate the error of the Taylor series after second non-zero term, if x = .
d) Using your calculator, sketch a graph of f(x) = cos x and the two non-zero term Taylor explansion.
1
2. Consider the function g(x) = 1−𝑥2
a) Taylor Series expansion of g to see the pattern of terms.
b) Calculate the interval of convergence for the Taylor series of g.
Math 272
Group Quiz
Name
3. Develop a quadratic Taylor series approximation for the function f(x,y) =cos(x2+y2) at (x,y) = (0,0).
4. Find and classify critical points for the function f(x,y) =(x+y)(xy+1). (problem 13, p. 798).