Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET20227 Aug 2022Morning ShiftMathematicsContinuity and DifferentiabilityActual

Give that f(x) cases = 1- 4 x x^2 & if x 0 cases at x=0 , then a=

Options

  1. A2
  2. B8
  3. C4
  4. D16

Correct answer

B. 8

Step-by-step solution

for continuity at x=0 aligned & _ x 0 1- 4 x x^2 =a= _ x 0 x 16+ x -4 & _ x 0 2 ^2 2 x (2 x)^2 4=a= _ x 0 x 16+ x -16 ( 16+ x +4) & a=8 aligned

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 MHT CET PYQs