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2. (7 points each) Find the exact value of each of the following limits. Write "..."...
2. (7 points each) Find the exact value of each of the following limits. Write".0,""-.0,"or "does not exist” if appropriate. It is particularly important to show your work on this problem. x3-4x a. lim x-2- x2-4x+4 2x4+4x b. lim X+0 3x4-4x+4 sin v c. lim X+0 VX
2. Evaluate (by SHOWING YOUR WORK!) the following limits. If the limit does not exist, write "does not exists": (a) (5 points) (You CANNOT use DE L'HOPITAL'S RULE!!) lim 1 - cos(x). 1-0 .22 (b) (5 points) You CAN use DE L'HOPITAL'S RULE!!) In(1 +6x) lim 2-0 C
2. Evaluate (by SHOWING YOUR WORK!) the following limits. If the limit does not exist, write "does not exists": (a) (5 points) (You CANNOT use DE L'HOPITAL's RULE!!) 1 – cos(x). lim 20 x2 (b) (5 points) You CAN use DE L'HOPITAL's RULE!!) In(1+6x) lim 10 2
Help on number 2 A-C Math 166 Spring 2020 Lab 12 - Integration Strategies and Improper Integrals 1. Evaluate the following integrals. (a) | In(x2 + 2a) dx 100 dx (8) Jo Je to (1) ["* sin(a) Vsee(2) de 5 1 11 x² – 2x – 3 dx 87/2 13 x(lnx)2 de (c) / tarda (1) [4x*e*** de 2. For what values of p do the following improper integrals converge? (1/2 da (0) Le 2 In () Jo 3. Give...
Integration by substitution 1. Find each of the following indefinite integrals using integration by substitution: dz (a) / (xºcos(x4) ) do (c) / (sin(2) cromka) die (e) / (24) do (a) / (2.eller) die (0) / (zlog.cz) Integration by parts 2. Find each of the following indefinite integrals using integration by parts: (a) / (+cos(x)) dx (c) / (vVy + 1) dy (e) / (sin”(w) ) at (8) / (sin(o) cos(0) ) da (b) / (x2=+) di (a) / (x2108_(2))...
2. Find the limits of the following functions if they exist. Show all necessary work. If the limit is co or -00, then state this rather than that it does not exist: (2 points each) a. lim x+3 V6x-2-4 x-3 b. lim arctan(3x) x sin(x) 3. Find the average value of the function f(x) = 4x2 + 8x -1 on (-1, 3).
3. Limits. The limits below do not exist. For each limit find two approach paths giving different limits Calculate the limits along each path. You may want to use Taylor series expansions to simplify the limits. sin (x) (1-cos (y) a) lim (y)(0,0 x+ PATH 1: LIMIT 1 PATH 2: LIMIT 2 b) lim (y)(8,0) cosx + In(1+ PATH 1: LIMIT 1 PATH 2: LIMIT 2 3. Limits. The limits below do not exist. For each limit find two approach...
1. (9 points) Referring to the graphs given below, use properties of limits to find each limit. If a limit does not exist then state that it does not exist. y = f(x) y = 8(%) R -1 - 1 -2 lim f(x) - lim g(x)- 10 10 lim x-0 g(x) lim f(x) - lim g(x)= lim (f(x) + g(x)]- lim f(x) - lim g(x) - 8(x) lim x- f(x)
Show detailed work 5. (8 points each) Find the limits: V3x2-6 (a) lim X--00 2x -9x (b) lim X-0.x2-sinx COS X (c) lim -X
1. Evaluate (by SHOWING YOUR WORK! You CANNOT use DE L'HOPITAL's RULE!!) the following limits. If the limit does not exist, write "does not exists": (a) (5 points) 2 - 31 lim 1++ 2.12 (b) (5 points) Vr-3 lim +91-9