displaystyle limxarrow0 (1/3-2(1)x) is equal to

Question

displaystyle limxarrow0 (1/3-2(1)x) is equal to (A) 0 (B) 1 (C) (1/2) (D) (1/3)

Tardigrade Admin · Accepted Answer

displaystyle lim x arrow 0- (1/3-21 / x) Put x =0-h ∴ displaystyle lim h arrow 0 (1/3-2(1)0-h) = displaystyle lim h arrow 0 (1/3-2-(1)h) =(1/3-2-(1)0)=(1/3-2-∞) =(1/3-0)=(1/3)

Q. $x \to 0 lim \frac{1}{3 - 2 ^{\frac{1}{x}}}$ is equal to

0

$1$

$\frac{1}{2}$

$\frac{1}{3}$

$- \infty$

$x \to 0^{-} lim \frac{1}{3 - 2 ^{1/ x}}$
Put $x = 0 - h$
$∴ h \to 0 lim \frac{1}{3 - 2 ^{\frac{1}{0 - h}}}$
$= h \to 0 lim \frac{1}{3 - 2 ^{- \frac{1}{h}}}$
$= \frac{1}{3 - 2 ^{- \frac{1}{0}}} = \frac{1}{3 - 2 ^{- \infty}}$
$= \frac{1}{3 - 0} = \frac{1}{3}$

Q. x→0lim​3−2x1​1​ is equal to

0

1

21​

31​

−∞

x→0−lim​3−21/x1​ Put x=0−h ∴h→0lim​3−20−h1​1​ =h→0lim​3−2−h1​1​ =3−2−01​1​=3−2−∞1​ =3−01​=31​

Q. $x \to 0 lim \frac{1}{3 - 2 ^{\frac{1}{x}}}$ is equal to

$1$

$\frac{1}{2}$

$\frac{1}{3}$

$- \infty$

$x \to 0^{-} lim \frac{1}{3 - 2 ^{1/ x}}$
Put $x = 0 - h$
$∴ h \to 0 lim \frac{1}{3 - 2 ^{\frac{1}{0 - h}}}$
$= h \to 0 lim \frac{1}{3 - 2 ^{- \frac{1}{h}}}$
$= \frac{1}{3 - 2 ^{- \frac{1}{0}}} = \frac{1}{3 - 2 ^{- \infty}}$
$= \frac{1}{3 - 0} = \frac{1}{3}$