can someone help me with this bound function and how to solve it. I dont get how my teacher did it.

Question

anonymous · Answer

$$\lim_{x \rightarrow \infty} \frac{ 3\cos x-\sin x }{ x-5}$$

anonymous · Answer

The absolute value of the top is clearly less than four, right?

anonymous · Answer

how do u know. he said its between -4 and 4..but idk how to get 4

anonymous · Answer

because cosine and sine are both always less than one.

anonymous · Answer

and greater than minus one.

anonymous · Answer

the way im thinking about iit is if the bound of sin and cos are -1 and 1 and there is a vertical stretch by 3,, then it becomes 4??? idk

anonymous · Answer

well the first term is clearly less than or equal to three, the second is less than or equal to one, so together they must be less than or equal to four.

anonymous · Answer

You may be overthinking it.