The value of Limx→∞2x−3x+1 is

Ltx→∞2x−3x+1=Ltx→∞x(2−3(1x))x(1+1x)As x→∞⇒1x→0=Lt1x→02−3(1x)1+(1x)=2−3(0)1+0=2

The value of Limx→∞2x−3x+1 is

Ltx→∞2x−3x+1=Ltx→∞x(2−3(1x))x(1+1x)As x→∞⇒1x→0=Lt1x→02−3(1x)1+(1x)=2−3(0)1+0=2

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The value of $\underset{x \to \infty}{L i m} \frac{2 x - 3}{x + 1}$ is

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Detailed Solution

$\underset{x \to \infty}{L t} \frac{2 x - 3}{x + 1} = \underset{x \to \infty}{L t} \frac{x (2 - 3 (\frac{1}{x}))}{x (1 + \frac{1}{x})}$

As $x \to \infty \Rightarrow \frac{1}{x} \to 0$

$= \underset{\frac{1}{x} \to 0}{L t} \frac{2 - 3 (\frac{1}{x})}{1 + (\frac{1}{x})} = \frac{2 - 3 (0)}{1 + 0}$ $= 2$

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The value of $\underset{x \to \infty}{L i m} \frac{2 x - 3}{x + 1}$ is