Evaluating $\lim_{t\to0} \tan(4t)/(2t)$

Question

$$\lim_{t\to0} \tan(4t)/(2t)$$

How would I evaluate that. I know that the limit of tan(t)/t = 1. How do I get the 4t to become a 2t inside the tangent?

Check this: http://en.wikipedia.org/wiki/L'H%C3%B4pital's_rule — Martijn Courteaux, Sep 08 '14 at 23:27

score 4 · Accepted Answer · answered Sep 08 '14 at 23:23

4

$$\lim_{t\to0} \tan(4t)/(2t)=2\lim_{4t\to0} \tan(4t)/(4t)=2$$

answered Sep 08 '14 at 23:23

mike

1

doesn't it seem like you would multiply by 1/2 though? – Sep 08 '14 at 23:32
yes. you multiply by 1/2 to complete the calculation of the limit. you then multiply the result by 2 to get back to original question. – mike Sep 08 '14 at 23:41

score 2 · Answer 2 · answered Sep 08 '14 at 23:23

2

Note that $$\frac{\tan(4t)}{2t}=2\cdot \frac{\tan(\color{red}{4t})}{\color{red}{4t}}$$ and that $4t\to 0$ when $t\to 0$.

answered Sep 08 '14 at 23:23

mathlove

2 Answers2