If f x is continuous in 0,1 and f 1 3 = 12 , then the value of lim n → ∞ ⁡ f n 3 n + 1 is equal to

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Question: Answered & Verified by Expert

If

f (x)

is continuous in

[0,1]

and

f (\frac{1}{3}) = 12

, then the value of

\lim_{n \to \infty} f (\frac{\sqrt{n}}{3 \sqrt{n} + 1})

is equal to

MathematicsContinuity and DifferentiabilityJEE Main

Options:

A $2$
B $3$
C $12$
D None of these

Solution:

1362 Upvotes Verified Answer

The correct answer is:

12

Since,

f (x)

is continuous in

[0,1]

, therefore,

\lim_{n \to \infty} f (\frac{\sqrt{n}}{3 \sqrt{n} + 1}) = f (\lim_{n \to \infty} \frac{\sqrt{n}}{3 \sqrt{n} + 1})

= f (\frac{1}{3}) = 12

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