If the function g(x)= … is differentiable, then the value of k+m is
JEE Main 2015 — Mathematics Calculus
2015mcqeasy
If the function g(x)={\begin{matrix}k\sqrt{x+1}\text{ , } & 0\leq x\leq 3 \\ mx+2 \text{, } & 3<x\leq 5\end{matrix} is differentiable, then the value of k+m is
Official previous-year question
Held on 4 Apr 2015 · Verified 6 Jul 2026.
Options
A
4
B
2
C
516
D
310
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Solution
LHD at x=3
x⟶3−lim(x−3kx+1−2k)
=x→3−limk(x−3x−3).x+1+21=4k
RHD at x=3
x→3+limx−3(mx+2)−2k
Since this limit exists if 3m+2−2k=0...(i) (00 form)
So,x→3+limx−3(mx+2)−(3m+2)=m
Hence m=4k…(ii)
From (i)&(\mathrm{ii})
m=\frac{2}{5} & k=\frac{8}{5} \Rightarrow k+m=2
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