# 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.

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### 1 Answer

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`