Solve the limit
https://i.gyazo.com/09217182d6523c8ffe3ae9197fcecd00.png

Question

Solve the limit 
https://i.gyazo.com/09217182d6523c8ffe3ae9197fcecd00.png

zepdrix · Answer

It appears this limit is approaching the indeterminate form 0/0.
Have you learned about L'Hospital's Rule? :)

anonymous · Answer

not yet

anonymous · Answer

the teacher told us to separate it

zepdrix · Answer

Ohhh ok interesting :)
Thanks for the hint.
So we'll do this...

zepdrix · Answer

Let's start by splitting up the 2,$$\large\rm \lim_{x\to0}\frac{1-\cos3x+1-\cos4x}{x}$$We'll break it up into two fractions, and then let's apply a limit law,$$\large\rm \lim_{x\to0}\frac{1-\cos3x}{x}+\lim_{x\to0}\frac{1-\cos4x}{x}$$

anonymous · Answer

how did you get two x's in the denominator? isn't that only possible if there's x^2?

zepdrix · Answer

No you silly billy :o$$\large\rm \frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}$$Remember how to combine and split up fractions? :)

zepdrix · Answer

We're `adding` the resulting fractions,
not multiplying.

Yes, if we had been multiplying, we would need 2 separate x's in the bottom.

zepdrix · Answer

$$\large\rm \frac{a\cdot b}{c\cdot c}=\frac{a}{c}\cdot\frac{b}{c}$$

zepdrix · Answer

Still stuck on that fraction business? :o
We have a couple tricky steps after that still.