Home
Class 12
MATHS
Let F (x,y) = (2x - 3y +4)/(x ^(2) + y ^...

Let `F (x,y) = (2x - 3y +4)/(x ^(2) + y ^(2) +4)` for all `(x,y) in R ^(2),` Show that f is continuous on `R ^(2).`

Text Solution

Verified by Experts

The correct Answer is:
0
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS AND PARTIAL DERIVATIVES

    NCERT TAMIL|Exercise EXERCISE 8.1|13 Videos

  • DIFFERENTIALS AND PARTIAL DERIVATIVES

    NCERT TAMIL|Exercise EXERCISE 8.2|17 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT TAMIL|Exercise MISCELLANEOUS EXERCISE|18 Videos

  • DISCRETE MATHEMATICS

    NCERT TAMIL|Exercise Exercise 12.3 (Choose the correct or the most suitable answer from the given four alternatives)|20 Videos

Similar Questions

Explore conceptually related problems

Let g(x,y) = (x^(2)y)/(x^(4) + y^(2)) for (x,y) ne (0,0) and f(0,0)=0. (i) Show that lim_((x,y) to (0,0)) g(x,y)=0 along every line y=mx, m in R . (ii) Show that lim_((x,y) to (0,0)) g(x,y) = k/(1+k^(2)) , along every parabola y=kx^(2), k in R{0} .

Let f(x, y) be a periodic function satisfying f(x, y) = f(2x + 2y, 2y-2x) for all x, y; Define g(x) = f(2^x,0) . Show that g(x) is a periodic function with period 12.

Show that f(x,y) = (x^(2)-y^(2))/(y^(2)+1) is continous at every, (x,y) in R^(2) .

Let f(x,y) = (y^(2) -xy)/(sqrt(x)-sqrt(y)) for (x,y) ne (0,0) . Show that lim_((x,y) to (0,0)) f(x,y) =0

Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is continuous at x=0, show that f(x) is continuous for all xdot

If (y^(2)-5 y)(x^(2)+2 x+4) lt 2 , for all x in R , then number of integers in the range of y is

Let f be a function such that f(x+y)=f(x)+f(y) for all xa n dya n df(x)=(2x^2+3x)g(x) for all x , where g(x) is continuous and g(0)=3. Then find f^(prime)(x)dot