Let f(x)= begincasesx sin ((1/x))+ sin ((1/x2)), x ≠ 0 0, x=0 endcases then displaystyle lim x arrow ∞ f(x) equals

Question

Let f(x)= begincasesx sin ((1/x))+ sin ((1/x2)), x ≠ 0 0, x=0 endcases then displaystyle lim x arrow ∞ f(x) equals (A) 0 (B) -1 / 2 (C) 1 (D) None of these

Tardigrade Admin · Accepted Answer

displaystyle lim x arrow ∞ f(x)= displaystyle lim x arrow ∞ x sin ((1/x))+ sin ((1/x2)) = displaystyle lim x arrow ∞ ( sin ((1/x))/((1)x))+ displaystyle lim x arrow ∞ sin ((1/x2)) =1+0=1

Q. Let $f (x) = {x sin (\frac{1}{x}) + sin (\frac{1}{x ^{2}}), 0, x \neq = 0 x = 0$
then $x \to \infty lim f (x)$ equals

0

-1 / 2

1

None of these

$x \to \infty lim f (x) = x \to \infty lim x sin (\frac{1}{x}) + sin (\frac{1}{x ^{2}})$
$= x \to \infty lim \frac{sin ( \frac{1}{x} )}{( \frac{1}{x} )} + x \to \infty lim sin (\frac{1}{x ^{2}})$
$= 1 + 0 = 1$

Q. Let f(x)={xsin(x1​)+sin(x21​),0,​x=0x=0​ then x→∞lim​f(x) equals

0

-1 / 2

1

None of these

x→∞lim​f(x)=x→∞lim​xsin(x1​)+sin(x21​) =x→∞lim​(x1​)sin(x1​)​+x→∞lim​sin(x21​) =1+0=1

Q. Let $f (x) = {x sin (\frac{1}{x}) + sin (\frac{1}{x ^{2}}), 0, x \neq = 0 x = 0$
then $x \to \infty lim f (x)$ equals

$x \to \infty lim f (x) = x \to \infty lim x sin (\frac{1}{x}) + sin (\frac{1}{x ^{2}})$
$= x \to \infty lim \frac{sin ( \frac{1}{x} )}{( \frac{1}{x} )} + x \to \infty lim sin (\frac{1}{x ^{2}})$
$= 1 + 0 = 1$