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Limits Continuity and Differentiability question

2024 · 31 Jan · Shift 1 · Q44

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JEE Main
Mathematics
Limits Continuity and Differentiability
2024 · 31 Jan · Shift 1 · Q44

Limits Continuity and Differentiability question

2024 · 31 Jan · Shift 1 · Q44

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let

g(x)

be a linear function and

f(x)=\left\{\begin{array}{cl}g(x) & , x \leq 0 \\ \left(\frac{1+x}{2+x}\right)^{\frac{1}{x}} & , x\gt 0\end{array}\right.

, is continuous at

x=0

. If

f^{\prime}(1)=f(-1)

, then the value

g(3)

is

A
$\log _e\left(\frac{4}{9}\right)-1$
B
$\frac{1}{3} \log _e\left(\frac{4}{9 e^{1 / 3}}\right)$
C
$\log _e\left(\frac{4}{9 e^{1 / 3}}\right)$
D
$\frac{1}{3} \log _e\left(\frac{4}{9}\right)+1$

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