Consider the function f(x)=\ array l ( 2 x)/(5 x) if x ≠ 0 (2)/(15) if x=0 array . Which one of the following is correct in respect of the function?

Correct answer: A. It is not continuous at x=0 _ x arrow 0 ( (2 x))/(5 x)= _ x arrow 0 ( (2 x)(2))/(5.(2 x))=(2)/(5) But at x=0, f(x)=(2)/(15) Hence, f(x) is not continuous at x=0 .

NDA 2018

Exam: NDA
Year: 2018
Subject: Mathematics
Chapter: Continuity and Differentiability

NDA 2018 · Mathematics · Continuity and Differentiability

Consider the function f(x)=\ array l ( 2 x)/(5 x) if x ≠ 0 (2)/(15)...

Consider the function

f(x)=\left\{

\begin{array}{l} \frac{\sin 2 x}{5 x} \text{ if } x \neq 0 \\ \frac{2}{15} \text{ if } x=0 \end{array}

\right.

Which one of the following is correct in respect of the function?

Options

AIt is not continuous at $x=0$
BIt is continuous at every x
CIt is not continuous at $x=\pi$
DIt is continuous at $x=0$

Correct answer

A. It is not continuous at $x=0$

Step-by-step solution

\lim _{x \rightarrow 0} \frac{\sin (2 x)}{5 x}=\lim _{x \rightarrow 0} \frac{\sin (2 x)(2)}{5.(2 x)}=\frac{2}{5}

But at

x=0, f(x)=\frac{2}{15}

Hence,

f(x)

is not continuous at

x=0

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 ? NDA 2026 Passage: Let f(x)= cases ax(x-1), & x 3 cases Given that f(x) is continuous for all x but… NDA 2026 Passage: Let f(x)= (x^2) and g(x)=x|x| for |x| Question: If q(x)=f ^ ∘ g(x) , then which… NDA 2026 Passage: Let f(x)= (x^2) and g(x)=x|x| for |x| Question: If p(x)=f(x)g(x) , then which of… NDA 2026 If f(x) is differentiable at x=a , then consider the following statements : I. f(x) is… NDA 2026 Passage: Let f(x)= cases ax(x-1), & x 3 cases Given that f(x) is continuous for all x but… NDA 2026 Consider the following for the two (02) items that follow: Let f(x) = cases x^3, & x^2… NDA 2025 For the following two (02) items: Let the function f(x) = |x - 3| + |x - 4| be defined on… NDA 2025 For the following two (02) items: Consider the function f(x) = cases 4(5^x), & x If the… NDA 2025 For the following two (02) items: Let the function f(x) = |x - 3| + |x - 4| be defined on… NDA 2025 Consider the following for the two (02) items that follow: Let f(x) = cases x^3, & x^2… NDA 2025 Paragraph: Let f(x)=[x]^2- [x^2] . Question: Consider the following statements: A. f(x)… NDA 2024 Let f(x)=|x|+1 and g(x)=[x]-1 , where [.] is the greatest integer function. Let… NDA 2024 Let f(x)=\ array cl (x-3)/(|x-3|)+a ; & x 3 array .f(x) be continuous at x=3 . What is… NDA 2023 Let f(x)=\ array cl (x-3)/(|x-3|)+a ; & x 3 array .f(x) be continuous at x=3 . What is… NDA 2023 Let f(x)=\ array cc a x(x+1)+b, & x < 1 x-1 & 1 ≤ x ≤ 2 array . If the function f(x) is… NDA 2023 Full Continuity and Differentiability list Continuity and Differentiability JEE Maths PYQs JEE Mathematics PYQs All NDA PYQs