Paragraph: Let f(x)=\ array cc x+6, & x ≤ 1 p x+q, & 1 Question: What is the value of p ?

Correct answer: B. 3 f(x)=\ array cc x+6, & x ≤ 1 p x+q, & 1 < x < 2 5 x, & x ≥ 2 array . f(x) is continuous LHL=RHL =f(1)1+6=p+qp+q=7 ....(1) LHL=RHL=f(2)p(2)+q=5(2)2 p+q=10 ....(2) (2) -(1), p=3

NDA 2023

Exam: NDA
Year: 2023
Subject: Mathematics
Chapter: Continuity and Differentiability

NDA 2023 · Mathematics · Continuity and Differentiability

Paragraph: Let f(x)=\ array cc x+6, & x ≤ 1 p x+q, & 1 Question:...

Paragraph: Let

f(x)=\left\{

\begin{array}{cc}x+6, & x \leq 1 \\ p x+q, & 1 < x < 2 \\ 5 x, & x \geq 2\end{array}

\right.

and

f(x)

is continuous.
Question: What is the value of

p

Options

A $2$
B $3$
C $4$
D $5$

Correct answer

B. $3$

Step-by-step solution

f(x)=\left\{

\begin{array}{cc}x+6, & x \leq 1 \\ p x+q, & 1 < x < 2 \\ 5 x, & x \geq 2\end{array}

\right.\because f(x)

is continuous

\therefore \quad

\mathrm{LHL}=\mathrm{RHL}

=f(1)1+6=p+qp+q=7

....(1)

\mathrm{LHL}=\mathrm{RHL}=f(2)p(2)+q=5(2)2 p+q=10

....(2) (2)

-(1), p=3

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