limy 1 0.05em( 1y^2-1- 2y^4-1)=

Correct answer: A. (a) Given, lim_y 1 0.05em( 1y^2-1- 2y^4-1)= lim_y 1 0.05em ( y^2+1-2y^4-1 ) = limy 1 0.05em ( y^2-1(y^2-1)(y^2+1) )= limy 1 0.05em 1y^2+1= 11+1= 12 .

JEE Previous Year Question

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

Topic: JEE PYQ

Answer: A. Full step-by-step solution below.

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

Correct answer: A

Solution

(a) Given, lim_{y \to 1} (\frac{1}{y ^{2} - 1} - \frac{2}{y ^{4} - 1}) = lim_{y \to 1} (\frac{y ^{2} + 1 - 2}{y ^{4} - 1}) = lim y \to 1 (\frac{y ^{2} - 1}{( y ^{2} - 1 ) ( y ^{2} + 1 )}) = lim y \to 1 \frac{1}{y ^{2} + 1} = \frac{1}{1 + 1} = \frac{1}{2} .

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