Question

What is the lim as x approaches zero sinx/x^2+3x?

Answer 1

Is that all in the denominator? (x^2+3x)

Answer 2

Yes that is all.

Answer 3

Factor the denominator:
\[\Large\bf\sf \lim_{x\to0} \frac{\sin x}{x(x+3)}\]We can write it like this,\[\Large\bf\sf =\lim_{x\to0}\frac{\sin x}{x}\cdot \lim_{x\to0}\frac{1}{x+3}\]

Answer 4

Does that first term look familiar?
It's an identity that you're supposed to remember! :D

Answer 5

Yes. sinx/x equals one. Special trig identity. So the answer is 1/3?

Answer 6

Yesssss, good job! :)

Answer 7

Thank you so much.!!!