Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2001MathematicsContinuity and Differentiability

If f(x)= x^2-10 x+25 x^2-7 x+10 and f is continuous at x=5 , then f(5) is equal to

Options

  1. A0
  2. B5
  3. C10
  4. D25

Correct answer

A. 0

Step-by-step solution

aligned f(5) & = _ x 5 f(x)= _ x 5 x^2-10 x+25 x^2-7 x+10 & = _ x 5 (x-5)^2 (x-5)(x-2) = _ x 5 x-5 x-2 & = 5-5 5-2 =0 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 AP EAMCET PYQs