Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2019MathematicsContinuity and DifferentiabilityActual

Consider the following statements in respect of the function f(x)= ( 1 x ) for x^1 0 and f(0)=0 ; 1. _ x 0 f(x) exists 2. f(x) is continuous at x=0 Which of the above statements is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

D. Neither 1 nor 2

Step-by-step solution

f(0)=0 and, f(x)= ( 1 x ) (i) _ x 0 f(x)= _ x 0 ( 1 x ) if x 0⁺ ; _ x 0⁺ ( 1 x )= if x 0⁻ ; _ x 0⁻ ( 1 x )=- - LHL RHL (ii) at x=0, LHL RHL f(x) is not continous both statements are wrong.

Practice Continuity and Differentiability on Quantrex Academy →

More from Continuity and Differentiability

What is the derivative of x |x| with respect to x , where x<0 ? 2026Passage: Let f(x)= cases ax(x-1), & x 3 cases Given that f(x) is continuous for all x but not differentiable at x=1 . Further f'(x) is continuous at x=3 . Question: What is the val 2026Passage: Let f(x)= (x^2) and g(x)=x|x| for |x| Question: If q(x)=f g(x) , then which of the following statements is/are correct ? I. q(x) is continuous at x=0 . II. q(x) is differe 2026Passage: Let f(x)= (x^2) and g(x)=x|x| for |x| Question: If p(x)=f(x)g(x) , then which of the following statements is/are correct ? I. p(x) is continuous at x=0 . II. p(x) is diffe 2026If f(x) is differentiable at x=a , then consider the following statements : I. f(x) is continuous at x=a II. _ x a f(x)=f(a) Which of the statements given above is/are correct ? 2026Passage: Let f(x)= cases ax(x-1), & x 3 cases Given that f(x) is continuous for all x but not differentiable at x=1 . Further f'(x) is continuous at x=3 . Question: What is the val 2026Consider the following for the two (02) items that follow: Let f(x) = cases x^3, & x^2 What is _ x 0 f'(x) equal to? 2025For the following two (02) items: Let the function f(x) = |x - 3| + |x - 4| be defined on the interval [0, 5] . What is dy dx at x = 3.5 equal to? 2025 Full Continuity and Differentiability list All NDA PYQs