

Exercise 5 (18 Points): Give a E 6 proof of each of the following statements: (A)...
3. (5pts each)Assume that a and b are constants. Evaluate each limit (MUST SHOW WORK!). If it does not exist, write DNE. lim (ax)2-12 Jax+b1 a. X- a b. lim X-00 5-4x V9x2+7 C. sin(2x) tan(6x) lim x0 x sin(3x) d. lim (e-* In(x)) x-00
explain clearly please
Problem 3 (6 points each). Evaluate the following limits algebraically, showing all work. If the limit does not exist, then write DNE and explain why it does not exist. You may use L'Hospial's rule but if you do you must specify that you have done so. (a) lim (e-2x + 2 tan-? (3.)) (5) limun (2+1) (c) lim a tan (1/1)
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
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...
QUESTION 15 Match each limit with the correct value. Some answers may be used more than once. 1 lim 2+ sin(x) 1. x → 2. Does Not Exist 3.1 lim x → 199² – 5x x2-5 4.2 5.0 4 lim (Vx2 + 2x - x) 6. - À lim (72x2 +3 - x)
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
Real analysis
10 11 12 13 please
(r 2 4.1 Limit of Function 129 se f: E → R, p is a limit point of E, and limf(x)-L. Prove that lim)ILI. h If, in addition, )o for all x E E, prove that lim b. Prove that lim (f(x))"-L" for each n E N. ethe limit theorems, examples, and previous exercises to find each of the following limits. State which theo- rems, examples, or exercises are used in each case....
2. (7 points each) Find the exact value of each of the following limits. Write "..." "-00," or "does not exist" if appropriate. It is particularly important to show your work on this problem 1 - 12 (a) lim 2+-1 2-1 12x + 1 (b) lim -100402 +9 sin?(0) (c) lim 3.12 1-0 4. Evaluate the following integrals 22/3 – x5/4 dx (a) (9 points) 1 (b) (8 points) / 72 (c) (8 points) / 9 sin() + cos(22) de...
1. (18 points) Determine if the following limits exist. In each case prove and explain your argument. (a) (0) lim ху 4xy? 2+(1,5) x+y lim **(0,0) x2 + y2 (b) x²y² lim *-*(0,0) *4 + 3y 2 (14 neinte) Find the derivative hole
just number 16
15-42 Find the limit or show that it does not exist. 1 x2 3x 15. lim 2 16. lim 3 x00 x x +1 2x+ 1 ズ→00 4x3 6x2- 2 x-2 17. lim 18. lim x21 2x3 4x
15-42 Find the limit or show that it does not exist. 1 x2 3x 15. lim 2 16. lim 3 x00 x x +1 2x+ 1 ズ→00 4x3 6x2- 2 x-2 17. lim 18. lim x21 2x3 4x