L'hopitals rule

Question

Use l'hopitals rule to solve:

Limit as x appriaches 0 of (tanx-x)/x

 

Answer 1

lim  tanx -x  =

x-0     x      

 

lim (tanx -x)' =

x-0     (x)'    

 

lim sec²x - 1 =

x-0        1

 

1 - 1 = 0

   1 

Answer 2

L'hopitals rule says if the limit is 0/0 then take the limit of derivative of the numerator and divide it by the limit of the derivative of denominator. 

 

So we have the limit as X goes to 0 of 

 

(sec² X -1)/1. As X goes to 0 the result is (1-1)/1 or 0. 

 

you can now apply this to the remaining problems that you have questions about.