Evaluate the limit. (If an answer does not exist, enter DNE.) lim 7 + et X-01-er
Evaluate lim ex, lim ex, and lime -X. X-00 X-00 X+00 lim ex = X-00 (Simplify your answer. Type an exact answer.)
2n2-31+1 b. lim cos 1. Find the following limits: a. lim 1 00 --- 3n2+4 n-00
Let f(x)-1 if XE [-1/2, 1 /2) x 2 if xE[1/2, T] If FN(x) is the partial sum of the Fourier series of f(x), then give lim Fv(1/2)? Please give your answer in decimal form. (Hint: It might be helpful to sketch the function)
Let f(x)-1 if XE [-1/2, 1 /2) x 2 if xE[1/2, T] If FN(x) is the partial sum of the Fourier series of f(x), then give lim Fv(1/2)? Please give your answer in decimal form. (Hint:...
Evaluate lim x--> infinity xe-x Justify your answer.
et (x) be a bounded sequence with positive terms. Show that lim(n2/x,) = +0
et (x) be a bounded sequence with positive terms. Show that lim(n2/x,) = +0
5. (8 points each) Find the limits: V3x2-6 (a) lim X-00 2x -9X (b) lim x=0x2-sinx COS X (c) lim x X- 2 2
16
Find the limit. lim (In xj8/x X-> 00 lim (In x)/x = (Simplify your answer.) X-00
Sketch the graph of the function f(r) with the following characteristics: lim f(x) = -00 lim f.) = -1 -2 0-0 lim f(x) =0 lim f(3) = -1 lim f (r) = 2 1-2
3. Evaluate the limits x-2 (a) lim 2 (c) lim x-,2x2 +2 ?- (b) lim 2 im 2x +4 (d) Given f(x)x1 -1<x s 2 3-?