Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202420 May 2024Morning ShiftMathematicsContinuity and DifferentiabilityActual

If a function f(x)= array cc ( +1) x+ 2 x x & if x 0 & at x=0 3 x- 3 x x^3 & if x 0 array . is continuous at x=0 then | |+| |=

Options

  1. A60
  2. B30
  3. C15
  4. D45

Correct answer

B. 30

Step-by-step solution

f^ (x) is continuous at x=0 _ x 0⁺ f(x)=f(0)= _ x 0⁺ ( +1) x+ 2 x x = +3= _ x 0⁻ f(x)= _ x 0⁻ f(x)= _ x 0⁻ 3 x- 3 x x^3 = _ x 0⁻ 3 3 x-3 ^2 3 x 3 x^2 = _ x 0⁻ -9 3 x- ^2 3 x 3 x 18 6 x =- 9 2 -9=- 27 2 = =- 27 2 -3=- 33 2 | |+| |= 60 2 =30

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