MHT CET202013 Oct 2020Morning ShiftMathematicsContinuity and DifferentiabilityActual

If the function f(x)= 1- 2 x+ 2 x 1+ 2 x+ 2 x if x 2 = k if x= 2 is continuous at x= 2 , then k =

Options

Correct answer

D. -1

Step-by-step solution

aligned _ x 2 f(x)=& _ x 2 1- 2 x+ 2 x 1+ 2 x+ 2 x =& _ x 2 (1+ 2 x)- 2 x (1+ 2 x)+ 2 x = _ x 2 2 ² x-2 x x x+2 x x =& _ x 2 2 x( x- x) 2 x( x+ x) = _ x 2 x- x x+ x = 0-1 0+1 =-1 aligned Since f(x) is continuous at x= 2 , we get k=-1

Practice Continuity and Differentiability on Quantrex Academy →

More from Continuity and Differentiability

The function f(x) = |x| + |x - 1| is: 2026 If f(x) = cases 1+x - 1-x x , & x 0 k, & x = 0 cases is continuous at x = 0 , then k = 2026 The function y = ||x| - 1| is differentiable for all values of ' x ' except 2026 Let 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? 2026 For 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 2026 If f(x) = cases ax + 7 & if x 1 cases is continuous at x = 1 , then 2026 If 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) = .......... 2026 Let [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