Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202314 May 2023Evening ShiftMathematicsContinuity and DifferentiabilityActual

The function f defined on (- 1 3 , 1 3 ) by f (x)= array cc 1 x ( 1+3 x 1-2 x ), & x 0 k & , x=0 array . is continuous at x=0 , then k is

Options

  1. A6
  2. B1
  3. C5
  4. D-5

Correct answer

C. 5

Step-by-step solution

f is continuous at x=0 . aligned f (0) & = _ x 0 f (x) k & = _ x 0 ( 1 x (1+3 x)- 1 x (1-2 x) ) & = _ x 0 ( 3 (1+3 x) 3 x + 2 (1-2 x) -2 x ) & =3+2=5 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