Lim x - 12 x-3-x-1-2 x2-x-3-IIT 1977-

The correct option is B 1/10 lim_x→ 1(2x 3)(√(x) 1) /(2x^2+x 3) On rationalisation lim_x→ 1(2x 3)(√(x) 1)×(√(x)+1) /(x 1)(2x+3)×(√(x)+1) = 1/5.2 = ...

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Byju's Answer

Standard XII

Mathematics

Rationalization Method to Remove Indeterminate Form

lim x → 12 x-...

Question

$l i m_{x \to 1}$ $\frac{(2 x - 3) (\sqrt{x} - 1)}{({2 x}^{2} + x - 3)}$ =
[IIT 1977]

-1/10

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1/10

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-1/8

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None of these

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Solution

The correct option is A
-1/10

$l i m_{x \to 1}$ $\frac{(2 x - 3) (\sqrt{x} - 1)}{({2 x}^{2} + x - 3)}$

On rationalisation -

$l i m_{x \to 1}$ $\frac{(2 x - 3) (\sqrt{x} - 1) \times (\sqrt{x} + 1)}{(x - 1) (2 x + 3) \times (\sqrt{x} + 1)}$

= $\frac{- 1}{5.2}$

= $\frac{- 1}{10}$

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Similar questions

lim x \to 1 \frac{(2 x - 3) (\sqrt{x} - 1)}{2 x^{2} + x - 3} =

lim x \to 1 \frac{(\sqrt{x} - 1) (2 x - 3)}{2 x^{2} + x - 3}

is equal to

lim x \to 1 \frac{(2 x - 3) (\sqrt{x} - 1)}{2 x^{2} + x - 3} .

\frac{- 1}{b}

Find b

(i) Evaluate $l i m x \to 1 \frac{(2 x - 3) (\sqrt{x} - 1)}{2 x^{2} + x - 3}$ (ii) Differentiate $\frac{x + s i n x}{x + c o s x}$ with respect to x.

lim x \to 1 \frac{(2 x - 3) (\sqrt{x} - 1)}{2 x^{2} + x - 3}

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limx→1(2x−3)(√x−1)(2x2+x−3) = [IIT 1977]

The correct option is A -1/10 limx→1(2x−3)(√x−1)(2x2+x−3) On rationalisation - limx→1(2x−3)(√x−1)×(√x+1)(x−1)(2x+3)×(√x+1) = −15.2 = −110

$l i m_{x \to 1}$ $\frac{(2 x - 3) (\sqrt{x} - 1)}{({2 x}^{2} + x - 3)}$ =
[IIT 1977]

The correct option is A
-1/10

$l i m_{x \to 1}$ $\frac{(2 x - 3) (\sqrt{x} - 1)}{({2 x}^{2} + x - 3)}$

On rationalisation -

$l i m_{x \to 1}$ $\frac{(2 x - 3) (\sqrt{x} - 1) \times (\sqrt{x} + 1)}{(x - 1) (2 x + 3) \times (\sqrt{x} + 1)}$

= $\frac{- 1}{5.2}$

= $\frac{- 1}{10}$