displaystyle lim x arrow ∞((x+6/x+1))x+4 is equal to

Question

displaystyle lim x arrow ∞((x+6/x+1))x+4 is equal to (A) e4 (B) e6 (C) e5 (D) e

Tardigrade Admin · Accepted Answer

displaystyle lim x arrow ∞((x+6/x+1))x+4= displaystyle lim x arrow ∞(1+(5/x+1))x+4 =e5 displaystyle lim x arrow ∞((x+4/x+1))=x5 displaystyle lim x arrow ∞((1+(4/x)/1+(1)x)) =e5

Q. $x \to \infty lim (\frac{x + 6}{x + 1})^{x + 4}$ is equal to

$e^{4}$

$e^{6}$

$e^{5}$

$e$

$x \to \infty lim (\frac{x + 6}{x + 1})^{x + 4} = x \to \infty lim (1 + \frac{5}{x + 1})^{x + 4}$
$= e^{5 x \to \infty lim (\frac{x + 4}{x + 1})} = x^{5 x \to \infty lim (\frac{1 + \frac{4}{x}}{1 + \frac{1}{x}})}$
$= e^{5}$

Q. x→∞lim​(x+1x+6​)x+4 is equal to

e4

e6

e5

e

x→∞lim​(x+1x+6​)x+4=x→∞lim​(1+x+15​)x+4 =e5x→∞lim​(x+1x+4​)=x5x→∞lim​(1+x1​1+x4​​) =e5

Q. $x \to \infty lim (\frac{x + 6}{x + 1})^{x + 4}$ is equal to

$e^{4}$

$e^{6}$

$e^{5}$

$e$

$x \to \infty lim (\frac{x + 6}{x + 1})^{x + 4} = x \to \infty lim (1 + \frac{5}{x + 1})^{x + 4}$
$= e^{5 x \to \infty lim (\frac{x + 4}{x + 1})} = x^{5 x \to \infty lim (\frac{1 + \frac{4}{x}}{1 + \frac{1}{x}})}$
$= e^{5}$