Solvelim(x->inf) [x2+x+1/2x2+x+1]sinx/x

BACK

Grade 12Integral Calculus

Solve
lim(x->inf) [x²+x+1/2x²+x+1]^sinx/x

Lovey

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

Ans:
Hello Student,
Please find answer to your question below

$L = \lim_{x\rightarrow \infty }(\frac{x^2+x+1}{2x^2+x+1})^{\frac{1}{x}}$
$L = \lim_{x\rightarrow \infty }(\frac{1+\frac{1}{x}+\frac{1}{x^2}}{2+\frac{1}{x}+\frac{1}{x^2}})^{\frac{1}{x}}$
$L = (\frac{1}{2})^{\lim_{x\rightarrow \infty }\frac{1}{x}}$
$L = (\frac{1}{2})^{0}$
$L = 1$