MHT CET20243 May 2024Morning ShiftMathematicsContinuity and DifferentiabilityActual

Let f (x)= 1- x 4 x- , x 4 , x [0, 1 2 ], f (x) is continuous in [0, 2 ] , then f ( 4 ) is

Options

A- 1 2
B1 2
C1
D-1

Correct answer

A. - 1 2

Step-by-step solution

aligned & f(x)= 1- x 4 x- & Let x= 4 + t & when x 4 , t 0 & f(x)= 1- ( 4 +t ) 4 ( 4 +t )- aligned aligned f(t) & = 1- ( 4 +t ) 4 t & = 1- ( 1+ t 1- t ) 4 t & = -2 t (1- t) 4 t = -1 2 t t 1 1- t f ( 4 ) & = _ t 0 f(t)= -1 2 aligned

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