Find the limit by the sandwich theorem

[Guest]

Find the limit by the sandwich theorem
[tex]\lim_{x\to0}\frac{sin(x)-xcos(x)}{x^3}[/tex]

[Jonasmathwork]

Solution: Given lim x->0 [sin(x)-xcos(x)]/x^3
by sandwich theorem we know that
g(x)≤f(x)≤h(x)
lim g(x)≤L≤lim h(x)

-1≤sin x≤+1
-1≤cosx≤+1
-x≤xcosx≤+x

-1-x≤sin x+x cos x≤1+x
-1-x/x3≤(sin x+x cos x)/x^3≤1+x/x^3

lim x-0(-1-x)/x^3=0
lim x-0 (1+x)/x^3=0

there for (sin x+x cos x)/x^3=0.

Hope you got your Answer.

[yasir2525]

nice post g....