how to calculate lim with sin?

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1 Answer
Jim H
Nov 8, 2017

The bit that takes some work is #(sen2x)/x# (pull the rest out of the way. (Factor the rest)

Explanation:

Use #lim_(thetararr0)sintheta/theta = 1#

#lim_(xrarr0)sin(2x)/x#

We want #theta = 2x#, so we need #2x# in the denominator.

# = lim_(xrarr0)2(sin(2x)/(2x))#

# = 2 lim_(xrarr0)(sin(2x)/(2x)) = 2(1) = 2#

#lim_(xrarr0) ((4x+6)/(2x-2) * 1/7) (sin(2x)/x) = (6/-2)(1/7)(2) = -6/7#

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