Home
Class 12
MATHS
lim( x to 0) ((1+5x^(2))/(1+3x^(2)))^(1...

` lim_( x to 0) ((1+5x^(2))/(1+3x^(2)))^(1//x^(2)) ` = … .

Text Solution

Verified by Experts

The correct Answer is:
`e^(2)`
` underset( x to 0) lim ((1+ 5x^(2))/(1+3x^(2)))^(1//x^(2))=(underset(x to 0) lim [(1+5x^(2))^(1//5 x^(2))]^(5))/(underset(x to 0) lim [( 1 + 3x^(2))^(1//3x^(2))]^(3)) = e^(5)/e^(3) = e^(2) `
Promotional Banner

Similar Questions

Explore conceptually related problems

lim_(x rarr0)((1+5x^(2))/(1+3x^(2)))^(1/x^(2))=

Evaluate lim_(xto0)((1+5x^(2))/(1+3x^(2)))^(1//x^(2))

lim_(x rarr0)((5x^(2)+1)/(3x^(2)+1))^(1/x^(2))

lim_(x rarr0)((1+5x)/(1+3x^(2)))^((1)/(x^(2)))

lim_(x rarr0)((1+x)^(5)-1)/(3x+5x^(2))

lim_(x rarr oo)((x^(2)+5x+3)/(x^(2)+x+3))^((1)/(x))

Evaluate: lim_ (x rarr oo) ((1 + 5x ^ (2)) / (1 + 3x ^ (2))) ^ (- x ^ (2))

lim_(x rarr0)((1)/(x sin^(-1)x)-(1-x^(2))/(x^(2)))