(r-2)2+2(y-1 )2 -2 +(y-1)for(x, y) (2,1) f(, y) for (a, y)(2, 1) 0 DNE lim а)...
(л +у)? )1 (а) Find or show that it doesn't exist lim (x,y)-(0,0) 2y2 (b) At what points in R2 is the function (x + y)2 if (r, y)(0,0), f(x,y) otherwise brief explanation continuous? Give a (л +у)? )1 (а) Find or show that it doesn't exist lim (x,y)-(0,0) 2y2 (b) At what points in R2 is the function (x + y)2 if (r, y)(0,0), f(x,y) otherwise brief explanation continuous? Give a
1. Suppose that lim x) = A, lim f(x) = B, 0) = C, where A, B, C are distinct real numbers. In each of the following, fill in the corresponding box by: • Expressing the limit in terms of A, B, C if it is possible to do so using the given information; • Writing DNE if it is possible to conclude that the limit does not exist using the given information; • Putting a X. otherwise. No explanation...
Sketch the graph of f(x) given the following: lim f(x) = 2 f(-1) =1 f(1) =1 lim f(x) = DNE 1--1 -> A function f is continuous at a number a if lim y(x) = f(a) ca requires the following 3 things:
Given that lim f(x) = 3, lim g(x) = 0, and lim h(x) = 5, find the limits that exist. Enter DNE if the limit doesn't exist help (limits) (a) lim f(x) + h(x)] = 8 (b) lim{f(x)} = 9 (c) lim yh(x) = 5^(1/3) help (limits) !!! help (limits) help (limits) In help (limits) help (limits) f(3) (2) (9) lim !!! help (limits) 3-a g(x) 2f(x) !! help (limits) h(x) - f(x)
3. Find lim f(,y) if it exists, and determine if f is continuous at (0,0. (x,y)--(0,0) (a) f(1,y) = (b) f(x,y) = { 0 1-y if(x, y) + (0,0) if(x,y) = (0,0) 4. Find y (a) 3.c- 5xy + tan xy = 0. (b) In y + sin(x - y) = 1.
41. (а) Let f(х, у) 2 + y2. Estimate fr(2,1) and fy(2, 1) using the contour diagram for f in Fig- ure 14.21 (b) Estimate fa (2, 1) and fy(2,1) from a table of values for f with (c) Compare your estimates in parts (a) and (b) with the exact values of fa (2,1) and fy(2,1) found al gebraically. 0.9, 1,1.1 1.9, 2, 2.1 andy y 3 2 1 -3 -1 2 3 -3 -2 1 Figure 14.21 T 41....
Sketch the graph of the function f(r) with the following characteristics: lim f(x) = -00 lim f.) = -1 -2 0-0 lim f(x) =0 lim f(3) = -1 lim f (r) = 2 1-2
using discrete structures 3. Consider the function F(x, y, z) for x, y, z z 0 defined as follows: a. F(x, y, 0)-y+1 b. F(x, 0, 1)-x c, F(x, 0, 2) = 0 d. F(x, 0, z+ 3)-1 e. F(x, y, z)-F(x, F(x, y-1, z), z-1) Using Induction, prove the following a. F(x, y, 1)-x +y b, F(x, y, 2) = xy c. F(x, y, 3)-xy 3. Consider the function F(x, y, z) for x, y, z z 0 defined...
Write DNE if the limit does not exist at a point. 1. lim g(x) = -1 Help on limits. 2. lim g(x) = 3 3. limg(x) = 0 M 4. lim g(x) = -4 5. g(1) = 2
Evaluate the double integral integral | | =+ wy? + rʻydA R where R= {(x,y) 1<x<2,1 <y<2} Double Integral Plot of integrand and Region R 300- 1] 1] 200 1] 100 0 -100 /1) /1) 0/1) 0/1) (0/1) 3/19 ersion -200 -300 101234 This plot is an example of the function over region R. The region and function identified in your problem slightly different Preview Answer Round your answer to four decimal places