displaystyle limy → 1 ( (1/y2 - 1) - (2/y4 - 1) ) =

Question

displaystyle limy → 1 ( (1/y2 - 1) - (2/y4 - 1) ) =  (A) (1/2) (B) (1/3) (C) (1/4) (D) 0

Tardigrade Admin · Accepted Answer

We have, displaystyle lim y arrow 1((1/y2-1)-(2/y4-1)) = displaystyle lim y arrow 1((y2+1-2/y4-1)) = displaystyle lim y arrow 1((y2-1/(y2-1)(y2+1))) = displaystyle lim y arrow 1 (1/y2+1)=(1/1+1)=(1/2)

Q. $y \to 1 lim (\frac{1}{y ^{2} - 1} - \frac{2}{y ^{4} - 1}) =$

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{4}$

0

We have, $y \to 1 lim (\frac{1}{y ^{2} - 1} - \frac{2}{y ^{4} - 1})$
$= y \to 1 lim (\frac{y ^{2} + 1 - 2}{y ^{4} - 1})$
$= y \to 1 lim (\frac{y ^{2} - 1}{( y ^{2} - 1 ) ( y ^{2} + 1 )})$
$= y \to 1 lim \frac{1}{y ^{2} + 1} = \frac{1}{1 + 1} = \frac{1}{2}$

Q. y→1lim​(y2−11​−y4−12​)=

21​

31​

41​

0

We have, y→1lim​(y2−11​−y4−12​) =y→1lim​(y4−1y2+1−2​) =y→1lim​((y2−1)(y2+1)y2−1​) =y→1lim​y2+11​=1+11​=21​

Q. $y \to 1 lim (\frac{1}{y ^{2} - 1} - \frac{2}{y ^{4} - 1}) =$

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{4}$

We have, $y \to 1 lim (\frac{1}{y ^{2} - 1} - \frac{2}{y ^{4} - 1})$
$= y \to 1 lim (\frac{y ^{2} + 1 - 2}{y ^{4} - 1})$
$= y \to 1 lim (\frac{y ^{2} - 1}{( y ^{2} - 1 ) ( y ^{2} + 1 )})$
$= y \to 1 lim \frac{1}{y ^{2} + 1} = \frac{1}{1 + 1} = \frac{1}{2}$