Question

Find the limit.

Answer 1

\[\lim_{x \rightarrow 0}\frac{ \sin5x }{ \tan3x }\]

Answer 2

\[\lim_{x \rightarrow 0}\frac{ sinx }{ x }=1\]
use this formula

Answer 3

@zemno i passed java starting to learn c++ in this semester :D

Answer 4

cool :)

Answer 5

what about your programming courses?

Answer 6

my first course of C++ finals will be next month

Answer 7

what compiler are you using?

Answer 8

codeblocks for now, since it is beginner friendly

Answer 9

oh we use microsoft visual 2008 c++

Answer 10

I could use microsoft visual studio 2015, since there is a free student account

Answer 11

for java eclipse

Answer 12

\[\frac{ \sin5x }{ 1 }*\frac{ 1 }{ \sin3x }*\frac{ \cos3x }{ 1 }\]

Answer 13

hint multiply by 15x/(15x)

Answer 14

No clue, how to multiply it by 15x/15x

Answer 15

\[\frac{\sin(5x)}{5x} \cdot \frac{3x}{\sin(3x)} \cdot \cos(3x) \cdot \frac{5}{3}\]

Answer 16

I multiply top and bot by 15x/(15x)
I hope you see why now

Answer 17

Could you show it directly? I don't see it

Answer 18

is it then 5/3?

Answer 19

yes because you have 1*1*1*5/3

Answer 20

or @Zenmo do you mean you don't see where I multiplied 15x/(15x)?

Answer 21

\[\frac{ 5x *\sin5x }{ 5x * 1 }* \frac{ 3x * 1 }{ 3x * \sin3x }*\cos3x\] thats what i tried to do just now, and yes; I don't see where you multipled 15x/15x

Answer 22

\[\frac{\sin(5x)}{\color{red}{5x}} \cdot \frac{\color{red}{3x}}{\sin(3x)} \cdot \cos(3x) \cdot \frac{\color{red}{5}}{\color{reD}3}\]

Answer 23

15x I wrote as 3x*5 on top
15x I wrote as 5x*3 on bot

Answer 24

you do what you did tooo... but you will just have to cancel x/x...
\[\frac{5 x \sin(5x)}{5x \cdot 1} \cdot \frac{3x \cdot 1}{3x \sin(3x)} \cdot \cos(3x) \\ 5x \cdot \frac{\sin(5x)}{5x} \cdot \frac{1}{3x} \cdot \frac{3x}{\sin(3x)} \cdot \cos(3x) \\ \frac{5x}{3x} \cdot \frac{\sin(5x)}{5x} \cdot \frac{3x}{\sin(3x)} \cdot \cos(3x) \\ \frac{5}{3} \cdot \frac{\sin(5x)}{5x} \cdot \frac{3x}{\sin(3x)} \cdot \cos(3x)\]
I hope you see I just used that multiplication is commutative in your answer (meaning I moved a lot of stuff around on top and on bot)

Answer 25

thanks! I see it now, on how you expanded mines

Answer 26

I'm not good at moving the numbers and fractions around yet.

Answer 27

just remember if you have multiplication you can move things around
example
\[\frac{a}{b} \cdot \frac{c}{d} \text{ is same as } \frac{a}{d} \cdot \frac{c}{b}\]

Answer 28

did you want to try another for more practive?

Answer 29

sure

Answer 30

\[\lim_{x \rightarrow 0} \frac{\cot(4x)}{\csc(2x)}\]

Answer 31

\[\frac{ \cos4x }{ 1 }* \frac{ 1 }{ \sin4x }* \frac{ \sin2x }{ 1 }\]
\[\frac{ \cos4x }{ 1 }*\frac{ 4x }{ 4x * \sin4x }*\frac{ 2x*\sin2x }{ 2x }\]
\[\frac{ 2x }{ 4x }=\frac{ 1 }{ 2 }\]

Answer 32

Done

Answer 33

you're good :)

Answer 34

I know how to do this easily by using L ' hospital rule, but professor wants to do it the standard way of using the formula sinx/x=1

Answer 35

thanks for the practice :)

Answer 36

the "standard way" is good too because it exercises your manipulation skills on algebra ... you will be a master manipulator of numbers