Question

Find the limit (if it exists)

Answer 1

\[\lim_{x \rightarrow \frac{ \pi }{ 4 }} \frac{ 4x }{ tanx}\]

Answer 2

what happens when you plug in x = pi/4?

Answer 3

no idea

Answer 4

\[\LARGE \lim_{x \to \frac{\pi}{4}}\frac{4x}{\tan(x)} = \frac{4*\left(\frac{\pi}{4}\right)}{\tan\left(\frac{\pi}{4}\right)}\]
\[\LARGE \lim_{x \to \frac{\pi}{4}}\frac{4x}{\tan(x)} = \frac{\cancel{4}*\left(\frac{\pi}{\cancel{4}}\right)}{\tan\left(\frac{\pi}{4}\right)}\]
\[\LARGE \lim_{x \to \frac{\pi}{4}}\frac{4x}{\tan(x)} = \frac{\pi}{\tan\left(\frac{\pi}{4}\right)}\]
I'll let you simplify the rest. Use the unit circle to find the value of tangent.

Answer 5

Unit Circle
https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/2000px-Unit_circle_angles_color.svg.png

Answer 6

\[\Large \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\]
\[\Large \tan\left(\frac{\pi}{4}\right) = \frac{\sin\left(\frac{\pi}{4}\right)}{\cos\left(\frac{\pi}{4}\right)}\]


Use the unit circle to locate the angle pi/4. Then find the sine and cosine of that angle. Divide the two values

Answer 7

Each point on the unit circle is of the form (x,y) where

x = cos(theta)
y = sin(theta)

Answer 8

oh ok

Answer 9

.76 and .65 ?

Answer 10

or you can use a calculator like this one

http://web2.0calc.com/

to compute `sin(pi/4)` and `cos(pi/4)`

make sure you're in radian mode

Answer 11

ok so after i do that what is next

Answer 12

what did you get for `sin(pi/4)` and `cos(pi/4)`

Answer 13

"what happens when you plug in x = pi/4?"
"no idea"

Seems like you need to review some trig, or algebra.