2. [4 marks each] Evaluate each of the following limits, if possible. Provide an appropriate analytic...
(4) Evaluate each of the following limits or show that the limit does not exist: (a lim 2014 – 2y4 (3,4) (0,0) 22 - y2 lim 1 + 2y (x,y) (0,0) = -2y (b)
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
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).
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
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
Evaluate the following limits.Can anyone help pls ? 3. Evaluate the following limits. i), e sinx lim (x,y)--(0,0) ii). lim (x,y)-(2,-3) iii). * lim (xy)--(0,0) lay] i. 1, ii. iii. - 1 i. 1, ii. iii. Limit does not exist 1. Limit does not exist, ii. iii. 3 i. 1, ii. iii. 1
4pts each] 9. Find the limit of the following if the limits exist. If not, explain x -3x+2 1) lim +4 r-1 11) lim 111) lim + 3x + 4 iv) lim :-*x-4 v) If 2x-15g(x)=x-2x+3, find limg(x)
1. (18 points) Determine if the following limits exist. In each case prove and explain your argument. (a) (c) lim *-(1,5) x+y 4.xy2 2+(0,0) x2 + y2 xy lim (b) x?y2 lim x-(0,0) x4 + 3y
5. (7 marks) Evaluate the limit, if it exists, or show that the limit does not exist. 51 + y 2.cy (a) lim (1,3)+(0,0) 5x + y + 9-3 (b), lim (x,y)+(0,0) x2 + y2
Question 2 (10 marks) In this question you must state if you use any standard limits, continuity, l'Hôpital's rule, the sandwich theorem or any convergence tests for series. You do not need to justify using limit laws 2n n3 or explain why it does not exist. (a) Evaluate lim n (b) Determine whether each of the following converge: n+3 2n (i) 2 (3n) (ii) (n3)! n=1 Question 2 (10 marks) In this question you must state if you use any...