Evaluate- x- 0lime1-x - 1e1-x - 1

The correct option is B 1 As it is ∞∞ form, applying L'hospital L = lim_x→ 0e^1/x( 1/x^2)e^1/x( 1/x^2) = 1 ⇒ (B) ...

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Differentiation under Integral Sign

Evaluate: x...

Question

Evaluate: $l i m x \to 0 \frac{e^{1 / x} - 1}{e^{1 / x} + 1}$

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I : lim x \to 0 [x] ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \frac{e^{\frac{1}{x}} - 1}{e^{\frac{1}{x}} + 1} ⎫ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎭

I I : lim x \to 0 ⎛ ⎜ ⎜ ⎜ ⎝ \frac{e^{\frac{1}{x}} - 1}{e^{\frac{1}{x}} + 1} ⎞ ⎟ ⎟ ⎟ ⎠

{lim}_{x \to 0} (\frac{e^{1 / x} - 1}{e^{1 / x} + 1})

lim x \to 0 \frac{e^{1 / x} - 1}{e^{1 / x} + 1}

lim x \to 0^{+} \frac{e^{1 / x} - 1}{e^{1 / x} + 1}

lim x \to 0 \frac{e^{1 / x} - 1}{e^{1 / x} + 1}

lim x \to 0 (\frac{e^{1 / x} - 1}{e^{1 / x} + 1})

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