Find limits for limx->0 (sin x)/(3x) Use L'Hospital's Rule when appropriate. If there is a more elementary algebraic method, you might consider itFind limits for lim x-->0   (sin x)/(3x)....

Find limits for limx->0 (sin x)/(3x) Use L'Hospital's Rule when appropriate. If there is a more elementary algebraic method, you might consider it

Find limits for lim x-->0   (sin x)/(3x). Use L'Hospital's Rule when appropriate. If there is a more elementary algebraic method, you might consider it.

If you are able to use L' Hopital's Rule and when you convert your expression to a fraction, check and state that the hypotheses of the theorem are satifsied. check problem by graphing the function near the limit and see if the values support the solution.

 

Asked on by cspanutius

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lfryerda | High School Teacher | (Level 2) Educator

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If you have already discussed the fundamental trig limit in class `lim_{x->0}{sin x}/x=1` then you can use it to evaluate this limit, otherwise you need to use L'Hopital's rule.

Method (1) with fundamental trig limit

`lim_{x->0}{sinx}/{3x}`

`=1/3 lim_{x->0} {sin x}/x`

`=1/3 \cdot 1`

`=1/3`

Method (2) using L'Hopital's rule

`lim_{x->0}{sin x}/{3x}`

`=lim_{x->0}{cos x}/{3}`  taking the derivative of num and denom here

`=1/3` 

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