Let f be a continuous function on R such that f(1 / 4 n)=( sin en) e-n2+(n2/n2+1) Then the value of f(0) is

Question

Let f be a continuous function on R such that f(1 / 4 n)=( sin en) e-n2+(n2/n2+1) Then the value of f(0) is (A) 1 (B) 1/2 (C) 0 (D) none of these

Tardigrade Admin · Accepted Answer

As f is continuous, f(0) = displaystyle lim x arrow 0 f(x) = displaystyle lim n arrow ∞ f(1 / 4 n) = displaystyle lim n arrow ∞(( sin en) e-n2+(1/1+1 / n2)) =0+1=1

Q. Let $f$ be a continuous function on $R$ such that $f (1/4 n) = (sin e^{n}) e^{- n^{2}} + \frac{n ^{2}}{n ^{2} + 1}$ Then the value of $f (0)$ is

1

1/2

0

none of these

As $f$ is continuous,
$f (0) = x \to 0 lim f (x)$
$= n \to \infty lim f (1/4 n)$
$= n \to \infty lim ((sin e^{n}) e^{- n^{2}} + \frac{1}{1 + 1/ n ^{2}})$
$= 0 + 1 = 1$

Q. Let f be a continuous function on R such that f(1/4n)=(sinen)e−n2+n2+1n2​ Then the value of f(0) is

1

1/2

0

none of these

As f is continuous, f(0)=x→0lim​f(x) =n→∞lim​f(1/4n) =n→∞lim​((sinen)e−n2+1+1/n21​) =0+1=1

Q. Let $f$ be a continuous function on $R$ such that $f (1/4 n) = (sin e^{n}) e^{- n^{2}} + \frac{n ^{2}}{n ^{2} + 1}$ Then the value of $f (0)$ is

As $f$ is continuous,
$f (0) = x \to 0 lim f (x)$
$= n \to \infty lim f (1/4 n)$
$= n \to \infty lim ((sin e^{n}) e^{- n^{2}} + \frac{1}{1 + 1/ n ^{2}})$
$= 0 + 1 = 1$