Home
Class 12
MATHS
Evaluate lim(xtooo) x^(3){sqrt(x^(2)+sqr...

Evaluate `lim_(xtooo) x^(3){sqrt(x^(2)+sqrt(1+x^(4)))-xsqrt(2)}.`

Text Solution

Verified by Experts

The correct Answer is:
`1//4sqrt(2)`
`underset(xtooo)limx^(3){sqrt(x^(2)+sqrt(1+x^(4)))-xsqrt(2)}`
`=underset(xtooo)limx^(3)[(x^(2)+sqrt(1+x^(4))-2x^(2))/(sqrt(x^(2)+sqrt(1+x^(4)))+xsqrt(2))]`
`=underset(xtooo)lim(x^(3))/((sqrt(x^(2)+sqrt(1+x^(4)))+xsqrt(2)))((1+x^(4)-x^(4)))/((sqrt(1+x^(4))+x^(2)))`
`=underset(xtooo)lim(x^(3))/((sqrt(x^(2)+sqrt(1+x^(4)))+xsqrt(2))(sqrt(1+x^(4))+x^(2)))`
`=underset(xtooo)lim(x^(3))/(x^(3)(sqrt(1+sqrt((1)/(x^(4))+1))+sqrt(2))(sqrt(1+(1)/(x^(4)))+1))`
`=(1)/(2sqrt(2)).1/2=(1)/(4sqrt(2))`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE|Exercise Exercise 2.4|5 Videos

  • LIMITS

    CENGAGE|Exercise Exercise 2.5|12 Videos

  • LIMITS

    CENGAGE|Exercise Exercise 2.2|7 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

Evaluate lim_(xtooo) x^((1)/(x)).

Evaluate lim_(xtooo) (1+(2)/(x))^(x).

Evaluate lim_(xto0)(sqrt(x^2+1)-1)/(sqrt(x^2+16)-4)

Evaluate: lim_(x to oo) (sqrt(x+2)-sqrt(2))/(x) .

lim_(xtooo)(1/x+2)

Evaluate lim_(xto5) (sqrt(x+4)-3)/(x-5)

Evaluate lim_(x to 0) (sqrt(1 +x^(2))-1)/x

Evaluate: lim_(x to infty) (sqrt(x^2+x+1)-sqrt(x^2+1))

Evaluate lim_(xto0)(sqrt(1+x)+sqrt(1-x))/(1+x)

lim_(xto oo)(sqrt(4x^(2)+2x+1)-sqrt(4x^(2)+1)) is