Home
Class 11
MATHS
Evaluate the following limits : Lim(x t...

Evaluate the following limits :
`Lim_(x to1/2)((8x-3)/(2x-1)-(4x^(2)+1)/(4x^(2)-1))`

Text Solution

Verified by Experts

Given, `underset(xto1//2)"lim"((8x-3)/(2x-1)-(4x^(2)+1)/(4x^(2)-1))= underset(xto1//2)"lim"[[(8x-3)(2x+1)-(4x^(2)+1))/(4x^(2)-1)]`
`=underset(xto1//2)"lim"[(16x^(2)+8x-6x-3-4x^(2)-1)/(4x^(2)-1)]`
`=underset(xto1//2)"lim"[(12x^(2)+2x-4)/(4x^(2)-1)]`
`=underset(xto1//2)"lim"(2(6x^(2)+x-2))/(4x^(2)-1)`
`=undersett(xto1//2)"lim"(2(6x^(2)+4x-3x-2))/(4x^(2)-1)`
`=underset(xto1//2)"lim"(2[2x(3x+2)-1(3x+2))]/(4x^(2)-1)`
`=underset(xto1//2)"lim"(2(3x+2)(2x-1))/((2x-1)(2x+1))`
`=underset(xto1//2)"lim"(2(3x+2))/(2x-1) = (2(3 xx 1/2 +2))/(2 xx 1/2+1)`
`=3/2+2=7/2`
Promotional Banner

Topper's Solved these Questions

  • LIMITS AND DERIVATIVES

    NCERT EXEMPLAR ENGLISH|Exercise LONG ANSWER TYPE QUESTIONS|11 Videos

  • LIMITS AND DERIVATIVES

    NCERT EXEMPLAR ENGLISH|Exercise OBJECTIVE TYPE QUESTIONS|23 Videos

  • INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

    NCERT EXEMPLAR ENGLISH|Exercise Fillers|16 Videos

  • LINEAR INEQUALITIES

    NCERT EXEMPLAR ENGLISH|Exercise Objective Type Questions|14 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following limits : Lim_(x to 1/2)(4x^(2)-1)/(2x-1)

Evaluate the following limits : Lim_(x to 1) (x^(2)-1)/(x-1)

Evaluate the following limits : Lim_(x to oo) (4x-3)/(2x+7)

Evaluate the following limits : lim_( x to 1/2) (4x^(2)-1)/(2x-1)

Evaluate the following limits : Lim_( x to 1) ((2x-3)(x-1))/(2x^(2)+x-3)

Evaluate the following limits : Lim_(x to -1) (x^(2)-1)/(x+1)

Evaluate the following limits : Lim_(xto1) (x-1)/(2x^(2)-7x+5)

Evaluate the following limits : Lim_(x to -1) ((x-4)(x+1))/(x^(2)+3x+2)

Evaluate the following limit: (lim)_(x->-1//2)(8x^3+1)/(2x+1)

Evaluate the following limit: (lim)_(x->-1//2)(8x^3+1)/(2x+1)