Determine if the limit exists, Graphically
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Determine if the limit exists, Graphically b.) lim X1 x2 + 3 2 x<> 1 x=1
If 4 - x2 = f(x) < 4+x2 for –3 <x<3, find lim (2) 20
Evaluate the following limit using Taylor series. 3 lim 2x2 zle x2 1 X>00
Find indicated quantity if it exists. La x + 3 if x < -2 54. Let f(x) Find IVx+ 2 if x > -2 (A) lim+ f(x) (B) lim-f(x) (C) lim, f(x) (D) f(-2) x-27
5. Evaluate the limit: lim expn n! n>00
2. For the difference cquation, X2+] = ax, + b = f(x,), where 0 <a < 1 and b> 0, use the solution given in (1.12) to find the following limit: lim ->XX7. Show that this limit is also a fixed point of the difference cquation, that is, it is a solution x of t = f(x) (see Figure 1.2).
X+2 X<3 n. lim f(x), where f(x)= { x3 12-2x x>3 3
Evaluate lim,-_-4+ g(x). 1 1 for -5< x < -4 X + 1 g(x) = 22 for X > -4 1 16 The limit does not exist. 1 3 -4
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-?
limit 3 HY) = -2+ aj evaluate_follo ning √x+124 b) for what value of a X2 is XZ1, X23 ${x) = { case Lax, *>3 continuous at everyx?
A. Express the limit as a definite integral on the given interval. B. Use the form of the definition of the integral to evaluate the integral. n Š lim n-> Xi Ax, [1, 3] (xi +13 * 2 i=1 3 6 (2x - x2) dx