Evaluate the limit. Be sure to show your reasoning. limit as x approaches 0 (sin7x / tan3x) ?
I know that the bottom turns to sin3x/cos3x and then i multiply the recipricol in which I get the limit as x approaches 0 (sin x7)(cos3x / sin 3x) but I don't know where to go from here :(
I know that the bottom turns to sin3x/cos3x and then i multiply the recipricol in which I get the limit as x approaches 0 (sin x7)(cos3x / sin 3x) but I don't know where to go from here :(
3 Answers
Explanation:
Explanation:
use L'HÃ´pital's Rule (also known as hospital's rule in English)
https://www.google.co.in/search?q=lhopital+rule&ie=&oe=
what this rule basically means is, if we have a limit for the division of two functions which looks like
therefore,
therefore, taking the derivative of both the functions, we get
=
which is equal to
now since
=
and
therefore, the limit is

Without using derivatives, see below.
Explanation:
As you have said:
# = (sin7x)/1 1/(sin3x) (cos3x)/1#
Now we'll write this so we can use
# = (sin7x)/(7x) * (7x)/(3x) (3x)/(sin3x) (cos3x)/1#
# =7/3 (sin7x)/(7x) (3x)/(sin3x) (cos3x)/1#
Now take limit as
# = 7/3 (1) (1) 1/1 = 7/3#