AP EAMCET202318 May 2023Evening ShiftMathematicsContinuity and DifferentiabilityActual

Let S_n=1+3 x+9 x^2+27 x^3+ n terms and - 1 3 < x < 1 3 If _ n S _ n = f ( x ) , then f ( x ) is discontinuous at the point x =

Options

A0
B1 3
C1
D-1

Correct answer

B. 1 3

Step-by-step solution

S _ n =1+3 x +9 x ^2+27 x ^3+ n terms aligned & _ n S_n=1+3 x+9 x^2+27 x^3+ & _ n S_n=(1-3 x)⁻¹= 1 1-3 x aligned So, f(x)= 1 1-3 x f ( x ) is discontinuous on x = 1 3

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 AP EAMCET PYQs