`lim_(x->oo)sechx` Find the limit

Friday, October 14, 2011

Given,

$\displaystyle\lim_{{{x}\to\infty}}$ sech(x)

to find the value of $\displaystyle\lim_{{{x}\to\infty}}$ sechx

we need to find the value of

$\displaystyle\lim_{{{x}\to-\infty}}$ sechx and $\displaystyle\lim_{{{x}\to+\infty}}$ sechx

so,

the value of

$\displaystyle\lim_{{{x}\to-\infty}}$ sechx is as x tends to negative infinity the sech(x) -> 0

and similarly as

$\displaystyle\lim_{{{x}\to+\infty}}$ sechx is as x tends to positive infinity the sech(x) -> 0

So,

$\displaystyle\lim_{{{x}\to-\infty}}$ sechx $\displaystyle=\lim_{{{x}\to+\infty}}$ sechx $\displaystyle={0}$

the limit exits for $\displaystyle\lim_{{{x}\to\infty}}$ sechx

and the value is $\displaystyle\lim_{{{x}\to\infty}}$ sechx=0

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