Question

Find the equation of the vertical and horizontal asymptotes if they exist for f(x)=(e^(sinx))/x.

Explain why.

Where do I begin?

Answer 1

you could do worse than starting with a sketch.

-1<= sin x < = 1 so that e term is not going to be doing a lot really. the dominant term will be the 1/x so at x+ -> 0 and x- -> 0 this could go nuts. the e term will always be positive (between e and 1/e), so you have the classix 1/x profile with some "wiggle" tending to zero both ways.

you can also calculate the derivative if that is where you are on the syllabus. that may or may not help but is always a good idea.