Home
Class 12
MATHS
Evaluate lim(xtooo) ((7x^(2)+1)/(5x^(2)-...

Evaluate `lim_(xtooo) ((7x^(2)+1)/(5x^(2)-1))^((x^(5))/(1-x^(3))).`

Text Solution

Verified by Experts

The correct Answer is:
0
`underset(xtooo)lim(7x^(2)+1)/(5x^(2)-1)=underset(xtooo)lim(7+(1)/(x^(2)))/(5-(1)/(x^(2)))=7/5`
`=underset(xtooo)lim(x^(5))/(1-x^(3))=underset(xtooo)lim(x^(2))/((1)/(x^(3))-1)=-oo`
`:." "underset(xtooo)lim((7x^(2)+1)/(5x^(2)-1))^((x^(5))/(1-x^(3)))=underset(xtooo)lim((7x^(2)+1)/(5x^(2)-1))^((x^(5))/(1-x^(3)))`
`=((7)/(5))^(-oo)=0`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE PUBLICATION|Exercise EXERCISE 2.4|5 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise EXERCISE 2.5|12 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise EXERCISE 2.2|7 Videos

  • JEE 2019

    CENGAGE PUBLICATION|Exercise Chapter 10|8 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE PUBLICATION|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

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

Evaluate lim_(xtooo) ((x^(2)+x-1)/(3x^(2)+2x+4))^((3x^(2)+x)/(x-2))

Evaluate lim_(xtooo) (sinx)/(x).

Evaluate lim_(xtooo) (log_(e)x)/(x)

Evaluate: ("lim")_(xtooo)x^(1/x)

Evaluate lim_(xtooo) (sqrt(25x^(2)-3x)+5x).

Evaluate: lim_(x->2) (x^2-1)/(2x+4)

Evaluate lim_(xto-oo)[(x^(4)sin((1)/(x))+x^(2))/((1+|x|^(3)))].

Evaluate: lim_(x rarr 0) (2^(3x)-1)/(3^(2x)-1)

Evaluate lim_(x to 0) ((x+4)/(2-x))^((x^(2)+2x-3)/(x-1))