NDA 2017 Maths · Mathematics · Continuity and Differentiability · easy

Let f(x)=(e^3x-1)/(2x) for x≠0 and f(0)=k. If f is continuous at x=0, then k equals

Single correct option

Let

f(x)=\frac{e^{3x}-1}{2x}

for

x\ne0

and

f(0)=k

. If

f

is continuous at

x=0

, then

k

equals

Show answer and solution

Answer: (D) $\frac32$

\lim_{x\to0}\frac{e^{3x}-1}{2x}=\frac32\lim\frac{e^{3x}-1}{3x}=\frac32

. Continuity needs

k=\frac32

. Using

\lim\frac{e^{3x}-1}{3x}=1

without the factor

\frac32

gives a wrong constant, and

0

comes from substituting

x=0

in the numerator only.

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