Home
Class 12
MATHS
Evaluate lim(xtosqrt(10)) (sqrt(7+2x)-(s...

Evaluate `lim_(xtosqrt(10)) (sqrt(7+2x)-(sqrt(5)+sqrt(2)))/(x^(2)-10).`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(2sqrt(10)"("sqrt(5)+sqrt(2)")")`
Rationalizing Nr., we get
`=underset(xtosqrt(10))lim(7+2x-(sqrt(5)+sqrt(2))^(2))/(x^(2)-10).(1)/(sqrt(7+2x)+(sqrt(5)+sqrt(2)))`
`= (1)/(sqrt(7+2sqrt(5))+(sqrt(5)+sqrt(2)))underset(xtosqrt(10))lim(2(x-sqrt(10)))/((x-sqrt(10))(x+sqrt(10)))`
`= (1)/((sqrt(5)+sqrt(2))+(sqrt(5)+sqrt(2))).(1)/(sqrt(10))`
`=(1)/(2sqrt(10)(sqrt(5)+sqrt(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

lim_(x rarr sqrt(10))(sqrt(7+2x)-(sqrt(5)+sqrt(2)))/(x^(2)-10) is equal to

Evaluate lim_(xto0) (sqrt(2+x)-sqrt(2))/(x).

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

lim_(x rarr sqrt(2))(sqrt(3+2x)-(sqrt(2)+1))/(x^(2)-2)

Evaluate lim_(x rarr2)(sqrt(x-2)+sqrt(x)-sqrt(2))/(sqrt(x^(2)-4))

Evaluate :lim_(x rarr2a^(+))(sqrt(x-2a)+sqrt(x)-sqrt(2a))/(x^(2)-4a^(2))

lim_(x rarr1)(sqrt(7x+2)-3)/(sqrt(5x-1)-sqrt(6x-2))

lim_(x->0)[((sqrt(x)-sqrt(7))(sqrt(x)+sqrt(7)))/(x-7)]

Evaluate, lim_(xtosqrt(2)) (x^(4)-4)/(x^7(2)+3sqrt(2x)-8) .

lim_(x rarr2)(sqrt(x-2)+sqrt(x)-sqrt(2))/(sqrt(x^(2)-4))