Limit of a trigonometric thing

[Jan Hill]

Homework Statement

Find the limit as x approaches zero of xcsc4x = the numerator over cos17x = the denominator

Homework Equations

The Attempt at a Solution

I don't know how to start except maybe multiplying both numerator and denominator by 4

 

[Mark44]

This?
$$\lim_{x \to 0} \frac{x~csc(4x)}{cos(17x)}$$

Start with some trig identities, such as csc(x) = 1/sin(x). There are some trig limits that will be helpful, such as lim sin(x)/x = 0, as x --> 0.

 

[Jan Hill]

so does this become lim as x approaches 0 of x times 1/sin(4x)
and this is lim as x approaches 0 of x/sin(4x)

and what trig limit should I use to deal with the denominator?


and please accept my many thanks for your quick reply of earlier!

 

[Mark44]

so does this become lim as x approaches 0 of x times 1/sin(4x)
and this is lim as x approaches 0 of x/sin(4x)

That's part of it.

It would be helpful if you wrote actual mathematics equations and expressions, rather than verbose English descriptions.

and what trig limit should I use to deal with the denominator?


and please accept my many thanks for your quick reply of earlier!