The value of l i m x → 0 - 2 1 x + 2 3 x 3 2 1 x + 5 2 3 x is, 1 3, 1 5, 1, 1 4

l i m x → 0 - 2 1 x 1 + 2 2 x 2 1 x 3 + 5 ⋅ 2 2 x ⇒ l i m x → 0 - 1 + 2 1 x 3 + 5 2 2 x = 1 + 0 3 + 0 = 1 3

The value of l i m x → 0 - 2 1 x + 2 3 x 3 2 1 x + 5 2 3 x is

Question: Answered & Verified by Expert

The value of

\underset{x \to 0^{-}}{l i m} \frac{2^{\frac{1}{x}} + 2^{\frac{3}{x}}}{3 (2^{\frac{1}{x}}) + 5 (2^{\frac{3}{x}})}

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Options:

Solution:

1179 Upvotes Verified Answer

The correct answer is:

\frac{1}{3}

\underset{x \to 0^{-}}{l i m} \frac{2^{\frac{1}{x}} \{1 + 2^{\frac{2}{x}}\}}{2^{\frac{1}{x}} \{3 + 5 \cdot 2^{\frac{2}{x}}\}} \Rightarrow \underset{x \to 0^{-}}{l i m} \frac{1 + 2^{\frac{1}{x}}}{3 + 5 (2^{\frac{2}{x}})}

= \frac{1 + 0}{3 + 0} = \frac{1}{3}

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