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

1 Answer
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.