How do you evaluate the limit #sinx/(7x)# as x approaches #0#?

1 Answer
martin23239
Mar 2, 2018

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad lim_{ x rarr 0 } sinx/{ 7 x } \ = \ 1/7. #

Explanation:

# "This follows as:" #

# \qquad \qquad lim_{ x rarr 0 } sinx/{ 7 x } \ = \ 1/7 cdot lim_{ x rarr 0 } sinx/x #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ = \ 1/7 cdot \underbrace{ lim_{ x rarr 0 } sinx/x }_{ "fundamental trig limit" = 1 } #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ = \ 1/7 cdot 1 \ = \ 1/7. #

# "Thus:" #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ lim_{ x rarr 0 } sinx/{ 7 x } \ = \ 1/7. #

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