displaystyle limx → 0 (x/|x|+x2) is equal to

Question

displaystyle limx → 0 (x/|x|+x2) is equal to (A) 1 (B) -1 (C) 0 (D) Does not exist

Tardigrade Admin · Accepted Answer

displaystyle lim x arrow 0- f(x)= displaystyle lim h arrow 0 (0-h/h+h2) = displaystyle lim h arrow 0 (-1/1+h)=-1 and displaystyle lim x arrow 0+ f(x)= displaystyle lim h arrow 0 (h/h+h2)= displaystyle lim h arrow 0 (1/1+h)=1 Hence, limit does not exist.

Q. $x \to 0 lim$ $\frac{x}{∣ x ∣ + x ^{2}}$ is equal to

1

-1

0

Does not exist

$x \to 0^{-} lim f (x) = h \to 0 lim \frac{0 - h}{h + h ^{2}}$
$= h \to 0 lim \frac{- 1}{1 + h} = - 1$
and $x \to 0^{+} lim f (x) = h \to 0 lim \frac{h}{h + h ^{2}} = h \to 0 lim \frac{1}{1 + h} = 1$
Hence, limit does not exist.

Q. x→0lim​ ∣x∣+x2x​ is equal to

1

-1

0

Does not exist

x→0−lim​f(x)=h→0lim​h+h20−h​ =h→0lim​1+h−1​=−1 and x→0+lim​f(x)=h→0lim​h+h2h​=h→0lim​1+h1​=1 Hence, limit does not exist.

Q. $x \to 0 lim$ $\frac{x}{∣ x ∣ + x ^{2}}$ is equal to

$x \to 0^{-} lim f (x) = h \to 0 lim \frac{0 - h}{h + h ^{2}}$
$= h \to 0 lim \frac{- 1}{1 + h} = - 1$
and $x \to 0^{+} lim f (x) = h \to 0 lim \frac{h}{h + h ^{2}} = h \to 0 lim \frac{1}{1 + h} = 1$
Hence, limit does not exist.