displaystyle lim x arrow 0 xx is equal to

Question

displaystyle lim x arrow 0 xx is equal to (A) 0 (B) 1 (C) -1 (D) None of these

Tardigrade Admin · Accepted Answer

Let y= displaystyle lim x arrow 0 xx ⇒ log y= displaystyle lim x arrow 0 x log x = displaystyle lim x arrow 0 ( log x/1 / x) ((∞/∞). form ) = displaystyle lim x arrow 0 (1 / x/-1 / x2) =- displaystyle lim x arrow 0 x=0 ⇒ y=e0=1 .

Q. $x \to 0 lim x^{x}$ is equal to

0

1

-1

None of these

Let $y = x \to 0 lim x^{x}$
$\Rightarrow lo g y = x \to 0 lim x lo g x$
$= x \to 0 lim \frac{lo g x}{1/ x} (\frac{\infty}{\infty}$ form $)$
$= x \to 0 lim \frac{1/ x}{- 1/ x ^{2}}$
$= - x \to 0 lim x = 0$
$\Rightarrow y = e^{0} = 1.$

Q. x→0lim​xx is equal to

0

1

-1

None of these

Let y=x→0lim​xx ⇒logy=x→0lim​xlogx =x→0lim​1/xlogx​ (∞∞​ form ) =x→0lim​−1/x21/x​ =−x→0lim​x=0 ⇒y=e0=1.

Q. $x \to 0 lim x^{x}$ is equal to

Let $y = x \to 0 lim x^{x}$
$\Rightarrow lo g y = x \to 0 lim x lo g x$
$= x \to 0 lim \frac{lo g x}{1/ x} (\frac{\infty}{\infty}$ form $)$
$= x \to 0 lim \frac{1/ x}{- 1/ x ^{2}}$
$= - x \to 0 lim x = 0$
$\Rightarrow y = e^{0} = 1.$