Find the indicated limit by using the limitslim(x, y) → (a, b)[f(x, y) - g(x, y)]lim(x,y) → (a, b)f(x, y) = 9 andlim(x,y) → (a, b) 9(x, y) = 16.

Answered: Image /qna-images/answer/2f8b606f-4438-459e-9331-dfb77fd4adc7.jpg

Answered: Find the indicated limit by using the…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

See similar textbooks

Similar questions

If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?
Find the limit (if it exists). If the limit does not exist, explain why. lim (xy+yz^2+xz^2/x^2+y^2+z^2) (x,y,z)--->(0,0,0)
Compute the limit (x,y)→(0,0) of 8xy / 2x^2+ 4y^2 along the following paths. (a) Along the y-axis. (b) Along the line y=3x. (c) What can you conclude about the limit?
Let f(x,y,z)=x^2+4y^2+2z^2. Does the limit lim_(0,0,0)f(x,y,z) exist? If so, use generalized to 3 dimension to show that this is the limit.
What does it mean for a function ƒ(x, y) to have limit L as (x, y) → (x0 , y0)? What are the basic properties of limits of functions of two independent variables?
Let f(x, y) = xy /(x 2 + y2). Show that f(x, y) approaches zero along the x- and y-axes. Then prove that lim f(x, y) does not exist by (x,y) (0,0)showing that the limit along the line y =xis nonzero.
By considering different paths, show that the limit doesn’t exist. a) lim (x,y)→(0,0) x2+y/ y b) lim (x,y)→(0,0) xy cos y/ 3x2+y2 c) lim (x,y)→(0,0) xy4/ x2+y8 d) lim (x,y)→(0,0) x2yey/ x4+4y2
consider a function f, defined by f(x,y) = -y/√x2+y2 what is the behavior of f along the line y=x when x>o; that is, what is the value of f(x,x) when x>0? If we approach (0,0) by moving along the line y=x in the first quadrant(thus considering f(x,x) as x→0+, what value do we find for the limit?
How do I show that the limit as (x,y) -> (0,0) does not exist for (x^2 - 4y^2)/(y^2)?
find the limit of ƒ as (x, y) →(0, 0) or show that the limit does not exist. ƒ(x, y) = y2/(x2 + y2)
Let f (x, y) = xy/(x2 + y2). Show that f (x, y) approaches zeroalong the x- and y-axes. Then prove that lim (x,y)→(0,0)f (x, y) does not exist by showing that the limit along the line y = x is nonzero.
Show that the function f(x,y)=x^4y/x^8+y^4 does not have a limit at (0,0) by examining the following limits. (a) Find the limit of f as (x,y)→(0,0) along the line y=x (b) Find the limit of f as (x,y)→(0,0) along the curve y=x^4

SEE MORE QUESTIONS

Recommended textbooks for you

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

SEE MORE TEXTBOOKS

Find the indicated limit by using the limits lim (x,y) → (a, b) [f(x, y) - g(x, y)] lim (x, y) → (a, b) f(x, y) = 9 and lim (x,y) → (a, b) 9(x, y) = 16.