Home
Class 12
MATHS
Prove that the function f(x) = x^n, is c...

Prove that the function `f(x) = x^n`, is continuous at `x=n`, where n is a positive integer.

Text Solution

Verified by Experts

The correct Answer is:
f is continuous at `n in N`.
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    OMEGA PUBLICATION|Exercise IMPORTANT QUESTIONS FROM MISCELLANEOUS EXERCISE|10 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OMEGA PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS |11 Videos

  • APPLICATION OF INTEGRALS

    OMEGA PUBLICATION|Exercise Multiple Choice Questions|16 Videos

  • DETERMINANTS

    OMEGA PUBLICATION|Exercise Multiple Choice Questions (MCQs)|20 Videos

Similar Questions

Explore conceptually related problems

Prove that the function f(x) = 5x-3 is continuous at x = 0

Prove that the function f(x) = 6x - 9 is continuous at x = 3 .

Prove that the function f(x) = x + |x| is continuous at x = 0 .

Prove that the function f(x) = x^(2n) + 1 is continuous at x = n , n > 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

Write the middle term in the expansion of : (1+x)^(2n) , where n is a positive integer.

Prove that the function f defined by f(x) = x^3 + x^2 -1 is a continuous function at x= 1.

Using Permutation or otherwise, prove that ((n^2)!)/((n!)^2) is an integer, where n is a positive integer.

The function f(x)=x-[x] , where [⋅] denotes the greatest integer function is (a) continuous everywhere (b) continuous at integer points only (c) continuous at non-integer points only (d) differentiable everywhere