Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Continuity and Differentiability

NDA 2015 · Mathematics · Continuity and Differentiability

Consider the function f(x)=\ array ccc a x-2 & for & -2 < x < -1 -1...

Consider the function f(x)=\left\{ax−2 for −2<x<−1−1 for −1≤x≤1a+2(x−1)2 for 1<x<2\begin{array}{ccc} a x-2 & \text{ for } & -2 < x < -1 \\ -1 & \text{ for } & -1 \leq x \leq 1 \\ a+2(x-1)^2 & \text{ for } & 1 < x < 2 \end{array}\right. What is the value of a for which f(x)f(x) is continuous at x=−1x=-1 and x=1\mathrm{x}=1 ?

Options

  1. A-1
  2. B1
  3. C0
  4. D2

Correct answer

A. -1

Step-by-step solution

f(x)=\left\{ax−2−2<x<−1−1−1≤x≤1a+2(x−1)21<x<2\begin{array}{cc} a x-2 & -2 < x < -1 \\ -1 & -1 \leq x \leq 1 \\ a+2(x-1)^2 & 1 < x < 2 \end{array}\right.$ if $f(x)$ is continuous at $x=-1$ then, \lim _{x \rightarrow-1}(a x-2)=\lim _{x \rightarrow-1}(-1)\begin{aligned} & \Rightarrow \mathrm{a}(-1)-2=-1 \\ & \Rightarrow \mathrm{a}=-1 \end{aligned}$ if $f(x)$ is continuous at $x=1$ then, $\lim _{x \rightarrow 1}$ a+2(x-1)^2=$\lim _{x \rightarrow 1}$-1\begin{aligned} & \Rightarrow \mathrm{a}+2(1-1)^2=-1 \\ & \Rightarrow \mathrm{a}=-1 \end{aligned}$$
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 2026Passage: Let f(x)= cases ax(x-1), & x 3 cases Given that f(x) is continuous for all x but… NDA 2026Passage: Let f(x)= (x^2) and g(x)=x|x| for |x| Question: If q(x)=f ^ ∘ g(x) , then which… NDA 2026Passage: Let f(x)= (x^2) and g(x)=x|x| for |x| Question: If p(x)=f(x)g(x) , then which of… NDA 2026If f(x) is differentiable at x=a , then consider the following statements : I. f(x) is… NDA 2026Passage: Let f(x)= cases ax(x-1), & x 3 cases Given that f(x) is continuous for all x but… NDA 2026Consider the following for the two (02) items that follow: Let f(x) = cases x^3, & x^2… NDA 2025For the following two (02) items: Let the function f(x) = |x - 3| + |x - 4| be defined on… NDA 2025For the following two (02) items: Consider the function f(x) = cases 4(5^x), & x If the… NDA 2025For the following two (02) items: Let the function f(x) = |x - 3| + |x - 4| be defined on… NDA 2025Consider the following for the two (02) items that follow: Let f(x) = cases x^3, & x^2… NDA 2025Paragraph: Let f(x)=[x]^2- [x^2] . Question: Consider the following statements: A. f(x)… NDA 2024Let f(x)=|x|+1 and g(x)=[x]-1 , where [.] is the greatest integer function. Let… NDA 2024Let f(x)=\ array cl (x-3)/(|x-3|)+a ; & x 3 array .f(x) be continuous at x=3 . What is… NDA 2023Let f(x)=\ array cl (x-3)/(|x-3|)+a ; & x 3 array .f(x) be continuous at x=3 . What is… NDA 2023Let 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 PYQsJEE Mathematics PYQs All NDA PYQs