_ y 1 (1 y^2-1 -2 y^4-1 )= - Vidyadip

MCQ

$\lim _{y \rightarrow 1}\left(\frac{1}{y^2-1}-\frac{2}{y^4-1}\right)=$

✓
$\frac{1}{2}$
B
$\frac{1}{3}$
C
$\frac{1}{4}$
D
$0$

✓

Answer

Correct option: A.

$\frac{1}{2}$

(A)
$\lim _{y \rightarrow 1}\left(\frac{1}{y^2-1}-\frac{2}{y^4-1}\right)$
$=\lim _{y \rightarrow 1}\left[\frac{1}{y^2-1}-\frac{2}{\left(y^2+1\right)\left(y^2-1\right)}\right]$
$=\lim _{y \rightarrow 1} \frac{y^2+1-2}{\left(y^2+1\right)\left(y^2-1\right)}$
$=\lim _{y \rightarrow 1} \frac{1}{y^2+1}$
$=\frac{1}{2}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Limits→Limits — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

In any $\triangle\text{ABC},\text{a}(\text{b}\cos\text{C}-\text{c}\cos\text{B})=$

The modulus and argument of $(1+ i \sqrt{ } 3)^8$ are respectively

If a circle, whose centre is (-1, 1) touches the straight line x + 2y + 12 = 0 then the co-ordinates of the point of contact are

A bag contains $3 $ red, $4$ white and $5$ blue balls. All balls are different. Two balls are drawn at random. The probability that they are of different colour is :

The value of $\sin^25^\circ+\sin^210^\circ+\sin^215^\circ+\ ...\ +\sin^285^\circ+\sin^290^\circ$ is :

If $e$ and $e^{\prime}$ are the eccentricities of the ellipse $5 x^2+9 y^2=45$ and the hyperbola $5 x^2-4 y^2=45$, then $ee ^{\prime}=$

$\lim _{x \rightarrow 0}\left[\frac{\log (5+x)-\log (5-x)}{\sin x}\right]=$

If $\text{A}=2\sin^2\text{x}-\cos2\text{x},$ then $A$ lies in the interval :

There are 5 girls and 2 boys, then the probability that no two boys are sitting together for a photograph is

If $A$ and $B$ are two sets such that $\text{n(A)}=70, \text{ n(B)}=60, \text{ n(A}\cup\text{B)}=110,$ then $\text{n(A}\cap\text{B)}$ is equal to :