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4. (10 pts) Evaluate the following limits: (a) lim h0 16+h - 4 h (b) limusin...
2. Evaluate the following limits. a) lim Vr+6-2 23 23 – 3.22 b) lim th h c) lim 3(2-2) cos(3) 22 +62 +9 h0 100
1. Evaluate each of the following limits: (4 pts ea) b) lim 2- a) lim VF-1 bilim 7-x
1. (10 pts) Evaluate limits. Apply L'Hopital's Rule when needed. (Inx) a. lim b. lim 1/(1-2) 20+
1. (8) Evaluate the following limits: (a) lim«;? () lim (6:1)".
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-?
Evaluate the following limits: x2 +7x - 14 a) lim 2x-5 b) lim tan(3x) - X = c) lim X+0 4x2-3r d) lim a "270 3x - 3xcos(2x) 2x2 sin(3x)
(4) Use MacLaurin series to evaluate the following limits. Do not use L'Hospital's rule. (a) lim-0 21+ucos g -3 sin e 136.23-1 (b) lim 0 sin(6x)(e-1-1)
Evaluate the following limits using l'Hôpital's Rule 10. lim sinx-2 x 7x3 10. lime sinti? 11. lim (1-3)* 12. lime e2-1 + 2x 12. lim 24-+2x 0
3. (5 pts. each) Evaluate the following limits if they exist. If the limit does not exist, then use the Two-Path Test to show that it does not exist. 5x²y (a) lim (x,y)=(0,0) **+3y2 (b) lim (x,y)-(1,-1) 1+xyz
Question 1 5 pts If F(x) = x + 4 which of the following limits is equal to F'(x). (Hint: Use the definition of the derivative.) O lim h 0 V ((x + 1) + 4 - V + 4 lim h 0 (a+h) +4 h lim h 0 √x+4+h- ſx + 4 h lim h-+0 V3+ 4+h h lim h-10 ✓(x + h) +4-x + 4 h M