Question

lim x-0 tanx/x

Answer 1

try to rewrite tan and then use a famous property ;)

Answer 2

\( \tan x = \sin x/ \cos x\)

Answer 3

simple substitution yields 0/0, which isnt a number

so use L'Hôpital's rule, differentiate the numerator and the denominator , then try subsitution again

Answer 4

i havent gotten there yet

Answer 5

\[
\frac{\tan x}{x} = \frac{\sin x}{x}\left(\frac{1}{\cos x}\right)
\]

Answer 6

\[\large \lim_{x \to 0 } \frac{\sin x}{x}=1 \]

Answer 7

You should know \[
\frac{\sin x}{x}
\]And \(1/\cos x\) is continuous.

Answer 8

\[\lim_{x\to0}\frac{\tan x}x \leadsto\frac00\\
\stackrel{\text{l'H}}
=\lim_{x\to0}\frac{\frac{\mathrm d}{\mathrm dx}{(\tan x)}}{\frac{\mathrm d}{\mathrm dx}(x)}\\
=\lim_{x\to0}\frac{\sec^2x}{1}\\={\sec^2(0)}\\=\frac1{\cos^2(0)}\\=\]