If f ( x ) = lim n → ∞ e x x 2 n + e − x e x + e − x x 2 n , which statement is true?

At x = 1 , f ( 1 ) = 1 . For x → 1 − , x 2 n → 0 and the value tends to e 2 ; for x → 1 + , x 2 n → ∞ and the value tends to e − 2 . Hence (D).

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Mathematics - Limits Question with Solution | TestHub

MathematicsLimitsGeneral ( Limit existence)Medium2 minQB

MathematicsMediumsingle choice

If $f (x) = lim_{n \to \infty} \frac{e ^{x} + e ^{- x} x ^{2 n}}{e ^{x} x ^{2 n} + e ^{- x}}$ , which statement is true?

Options:

Answer:

Solution:

At $x = 1, f (1) = 1$ . For $x \to 1^{-}, x^{2 n} \to 0$ and the value tends to $e^{2}$ ; for $x \to 1^{+}, x^{2 n} \to \infty$ and the value tends to $e^{- 2}$ . Hence (D).

Stream:JEESubject:MathematicsTopic:LimitsSubtopic:General ( Limit existence)

⏱ 2mℹ️ Source: QB

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