Home
Class 11
MATHS
If f(x) = mx^2+n, x lt o = nx+m, o le ...

If `f(x) = mx^2+n, x lt o`
`= nx+m, o le x le 1`
`= nx^3+m, x gt 1`
For what value of integers m,n does the limits `lim_( x to 0) f(x)` and `lim_(x to 1) f(x)` exist.

Promotional Banner

Topper's Solved these Questions

  • LIMIT, CONTINUITY AND DIFFERENTIABILITY

    PATHFINDER|Exercise QUESTION BANK|293 Videos
  • MATHEMATICAL REASONING

    PATHFINDER|Exercise QUESTION BANK|27 Videos

Similar Questions

Explore conceptually related problems

If f(x)={{:(mx^(2)+n",",xlt0),(nx+m",",0lexle1),(nx^(3)+m",",xgt1):} . For what integers m and n does both lim_(xrarr0)f(x) and lim_(xrarr1)f(x) exist?

If lim_(x->a)[f(x)g(x)] exists, then both lim_(xtoa)f(x) and lim_(x->a)g(x) exist.

The function f(x) =p [x+1] +q [x-1] where [x] is the greatest integer function, and lim _(xto1+) f(x) =lim _(x to 1-) f(x)= f(1) when-

Consider the following graph of the function y=f(x). Which of the following is//are correct? (a) lim_(xto1) f(x) does not exist. (b) lim_(xto2)f(x) does not exist. (c) lim_(xto3) f(x)=3. (d)lim_(xto1.99) f(x) exists.

If f(x)=sgn(x)" and "g(x)=x^(3) ,then prove that lim_(xto0) f(x).g(x) exists though lim_(xto0) f(x) does not exist.

Let f(x)=(bx+a)/(x+1), lim_(x to 0)f(x)=2 then the value of a is .

If f(x) = (p - x^n)^(1/n), p gt 0 and n is positive integer, then the value of f[f(x)]

Let f : R to R be a real function. The function f is double differentiable. If there exists ninN and p in R such that lim_(x to oo)x^(n)f(x)=p and there exists lim_(x to oo)x^(n+1)f(x) , then lim_(x to oo)x^(n+1)f'(x) is equal to

If f'(x) exists and if f'(x) lt 0 everywhere in the interval a le x le b , then show that f(x) is a decreasing function in a le x lt b .

Let f(x^m y^n)=mf(x)+nf(y) for all x , y in R^+ and for all m ,n in Rdot If f^(prime)(x) exists and has the value e/x , then find lim_(x->0)(f(1+x))/x