Posted by **Po** on Monday, November 21, 2016 at 9:44pm.

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it.

lim (tan(7x))^x

x~>0

- Calculus -
**Steve**, Monday, November 21, 2016 at 11:33pm
You know that lim sinu/u = 1

so, lim tanu/u = 1 (because lim cosu = 1)

So, lim tan(7x)/x

= lim (tan(7x)*7)/(7x)

= 7 lim tanu/u where u7x

= 7

or, using L'Hospital,

lim tan(7x)/x

= lim (7 sec^2(7x))/1

= 7

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