Evaluate- lim x - 1-1-x2-x-2-x-x2-1-A- undefinedB- undefinedC- undefinedD- undefined

lim_x → 1 [ 1/x^2+x 2 x/x^2 1 ] [ 1/(x 1)(x+2) x/(x 1)(x^2 + x+1) ] 1/x 1 [ 1/x+1 x/x^2+x+1 ] 1/x 1[x^2+2+1 (x^2+2x)/(x^2+2+1)(x+2) ] 1/x 1 [ 2x+x+1/(x^2+ ...

347

You visited us 347 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Other

Quantitative Aptitude

Functions

Evaluate: lim...

Question

Evaluate: $l i m_{x \to 1} [\frac{1}{x^{2} + x - 2} - \frac{x}{x^{2} - 1}]$

Open in App

Solution

$l i m_{x \to 1} [\frac{1}{x^{2} + x - 2} - \frac{x}{x^{2} - 1}]$
$[\frac{1}{(x - 1) (x + 2)} - \frac{x}{(x - 1) (x^{2} + x + 1)}]$
$\frac{1}{x - 1} [\frac{1}{x + 1} - \frac{x}{x^{2} + x + 1}]$
$\frac{1}{x - 1} [\frac{x^{2} + 2 + 1 - (x^{2} + 2 x)}{(x^{2} + 2 + 1) (x + 2)}]$
$\frac{1}{x - 1} [\frac{- 2 x + x + 1}{(x^{2} + x + 1) (x + 2)}]$
$\frac{1}{x - 1} [\frac{x + 1^{- 1}}{(x + 2) (x^{2} + x + 1)}]$
$= [\frac{- 1}{(x + 2) (x^{2} + 2 + 1)}]$
$l i m_{x \to 1} [\frac{- 1}{(x + 2) (x^{2} + x + 1)}]$
$= \frac{- 1}{(3) (1 + 1 + 1)}$
$= \frac{- 1}{9}$

Suggest Corrections

Similar questions

Q. Quardratic surds
If

x = \sqrt{\frac{\sqrt{5} + 1}{\sqrt{5} + 1}}

Then prove that

x^{2} - x - 1 = 0

s i n {2 t a n^{- 1} \sqrt{\frac{1 - x}{1 + x}}}

Q. Factorised :

x^{2} + 10 x + 20

Q. Divide

x^{2} - 9 x - 10 b y x + 1

. Write down all steps involved in division.

Q. Solve for x

(\frac{1}{p}) + (\frac{1}{q}) + (\frac{1}{x}) = \frac{1}{(x + p + q)}

Join BYJU'S Learning Program

Evaluate: limx→1[1x2+x−2−xx2−1]

limx→1[1x2+x−2−xx2−1] [1(x−1)(x+2)−x(x−1)(x2+x+1)] 1x−1[1x+1−xx2+x+1] 1x−1[x2+2+1 − (x2+2x)(x2+2+1)(x+2)] 1x−1[−2x+x+1(x2+x+1)(x+2)] 1x−1[x+1−1(x+2)(x2+x+1)] =[−1(x+2)(x2+2+1)] limx→1[−1(x+2)(x2+x+1)] =−1(3)(1+1+1) =−19

Evaluate: $l i m_{x \to 1} [\frac{1}{x^{2} + x - 2} - \frac{x}{x^{2} - 1}]$