Evaluate -lim-xrightarrow infty- dfrac-2x-3-x-5-

Question

Toppr Admin · Accepted Answer

Limx-x2192-x221E-2x-3x-x2212-5Put x-1yIf x-x2192-x221E-y-x2192-0Therefore-limx-x2192-x221E-2x-3x-x2212-5-limy-x2192-02y-31y-x2212-5-limy-x2192-02-3y1-x2212-5y-2-01-x2212-0-2-

Evaluate :
$l i m_{x \to \infty} \frac{2 x + 3}{x - 5}$ .

$l i m_{x \to \infty} \frac{2 x + 3}{x - 5}$

Put $x = \frac{1}{y}$
If $x \to \infty, y \to 0$

Therefore,
$l i m_{x \to \infty} \frac{2 x + 3}{x - 5} = l i m_{y \to 0} \frac{\frac{2}{y} + 3}{\frac{1}{y} - 5}$

$= l i m_{y \to 0} \frac{2 + 3 y}{1 - 5 y} = \frac{2 + 0}{1 - 0} = 2$ .

Evaluate :limx→∞2x+3x−5.

limx→∞2x+3x−5Put x=1yIf x→∞,y→0Therefore,limx→∞2x+3x−5=limy→02y+31y−5=limy→02+3y1−5y=2+01−0=2.

Evaluate :
$l i m_{x \to \infty} \frac{2 x + 3}{x - 5}$ .

$l i m_{x \to \infty} \frac{2 x + 3}{x - 5}$

Put $x = \frac{1}{y}$
If $x \to \infty, y \to 0$

Therefore,
$l i m_{x \to \infty} \frac{2 x + 3}{x - 5} = l i m_{y \to 0} \frac{\frac{2}{y} + 3}{\frac{1}{y} - 5}$

$= l i m_{y \to 0} \frac{2 + 3 y}{1 - 5 y} = \frac{2 + 0}{1 - 0} = 2$ .