Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2020MathematicsContinuity and Differentiability

If the function f(x)= array cl 1- x x² , & for x 0 k, & for x=0 array . is continuous at x=0 , then the value of k is

Options

  1. A0
  2. B1
  3. C-1
  4. D1 / 2

Correct answer

D. 1 / 2

Step-by-step solution

We have, f(x)= array cl 1- x x² , & x 0 k, & x=0 array . Since, f(x) is continuous at x=0 , then f(0)= _ x 0 f(x) k= _ x 0 1- x x² k= _ x 0 x 2 x [using L' Hospital Rule] k= 1 2

Practice Continuity and Differentiability on Quantrex Academy →

More from Continuity and Differentiability

The function f(x) = |x| + |x - 1| is: 2026If f(x) = cases 1+x - 1-x x , & x 0 k, & x = 0 cases is continuous at x = 0 , then k = 2026The function y = ||x| - 1| is differentiable for all values of ' x ' except 2026Let f : R R be the function given by f(x) = |x - 2| + 3|x - 1| + ||x - 2| - 1| . What is the number of points where f is NOT differentiable? 2026For real numbers a and b , consider the function f : R R given by f(x) = cases -ax - b & if x 1. cases How many pairs (a, b) are there for which f is continuous at every point of R 2026If f(x) = cases ax + 7 & if x 1 cases is continuous at x = 1 , then 2026If the function f(x) defined by f(x) = cases ax + 1 & if x 3 bx + 3 & if x > 3 cases is continuous at x = 3 , then (a - b) = .......... 2026Let [x] denotes the greatest integer less than or equal to x and f(x) = [ ^2 x] , then which of the following is true ? 2026 Full Continuity and Differentiability list All COMEDK PYQs