4. Find the limit of each function at the given point, or explain why it does not exist. (a) 1O p...
Find the limit or explain why it doesn't exist: 3. (8 marks) Find the limit or explain why the limit does not exist: (a) lim 1 + x - V1 - 2 2 (b) lim 2-3 2+2 2----2
f(x, y) = y/(sqrt(z? + y2) + x) Evaluate the limits below, if they exist. If the limit does not exist, explain why it does not exist Yon musi elearly staie if you ity, lopital's rle or the sandwch theorem in your working. You do not need to justify using limit laws. (i) lim f(x, y) (ii) im f(r, y (iv) zlin2-1.0 arctan ^Ca.v)l f(x, y) = y/(sqrt(z? + y2) + x) Evaluate the limits below, if they exist. If...
for each f and P below. If the limit does not exist, prove it. y sin X 1919) (x - y)2 + 2x – 1''.
Find the limit, if it exists, or show that the limit does not exist. 1. lim (x²y3 – 4y?) (2,y)+(3,2) 2. lim 24 - 4y2 (x,y)+(0,0) x2 + 2y2 3. Find the first partial derivatives of the function of f(x,y) = x4 + 5.cy 4. Find all the second partial derivatives of f(x,y) = x+y + 2.x2y3 5. Find the indicated partial derivatives. f(1, y) = x^y2 – røy ; farzz, fryz
(1 point) Find lim vx+10. If the limit increases or decreases without bound, write inf or -inf, respectively. If it does not exist and cannot be represented by +oo or -oo, enter DNE. i.) If the limit does not exist, explain why. Check ALL that apply: A. The function is not defined beyond a particular bound in the direction of-co B. The function's behavior as x increases/decreases without bound does not approach one set value (for example, if the function...
Find the limit algebraically, if it exists. If the limit does not exist, state that fact. x2 - 16 . 10x2 + 3 lim - x+-4 X+4 x + 2x + 1 i + lim -13 0 0 0 0 The limit does not exist.
4. (4 pts each) Find the limit, if it exists, of each sequence. Justify your answer. If the limit does not exist, state why. пт 3"-2" (a) an = sin (b) bn 4n - 3
evaluate each limit or explain why it does not exist (b) 4x² - y² lim (x,y)+(0,0) x2 + 2y2
Question 11 5 pts Find exact value the limit, if it exists. If the limit does not exist, type "dne" and explain why. lim sin(x-2) x2-4 = x + 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).