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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Continuity and Differentiability

NDA 2021 · Mathematics · Continuity and Differentiability

If the function f(x)=\ array ll a+b x, & x 1 array . is continuous,...

If the function f(x)=\left\{a+bx,x<15,x=1b−ax,x>1\begin{array}{ll}a+b x, & x < 1 \\ 5, & x=1 \\ b-a x, & x > 1\end{array}\right. is continuous, then what is the value of (a+b)(a+b) ?

Options

  1. A55
  2. B1010
  3. C1515
  4. D2020

Correct answer

A. 55

Step-by-step solution

f(x)=\left\{a+bx,x<15,x=1, is  continuous  b−ax,x>1\begin{array}{lc}a+b x, & x < 1 \\ 5, & x=1, \text{\text{ is }\text{ continuous } } \\ b-a x, & x > 1\end{array}\right.lim⁡x→1−f(x)=lim⁡x→1+f(x)=f(1)lim⁡x→1−(a+bx)=lim⁡x→1+(b−ax)=5\begin{aligned} & \lim _{x \rightarrow 1^{-}} f(x)=\lim _{x \rightarrow 1^{+}} f(x)=f(1) \\ & \lim _{x \rightarrow 1^{-}}(a+b x)=\lim _{x \rightarrow 1^{+}}(b-a x)=5\end{aligned}a+b=5…a+b=5\ldots (i)andb−a=5and b-a=5.\ldots(ii)From(i)and(ii)b=5anda=0∴a+b=0+5=5From (i) and (ii) b=5 and a=0\therefore a+\mathrm{b}=0+5=5
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