Quandaries
and Queries
Who is asking: Student
Level: Secondary
Question:
I have two questions, one about a limit and the other about a composite
function. If you could help me, I'd really appreciate it.
1. Find the limit:
lim[x->0] (x*csc(x))
I converted csc(x) to cos(x)/sin(x), but I didn't know what to do after that.
2. f(g(x)) = ln(x^2 + 4), f(x) = ln(x^2) and g(x) > 0 for all real x, find g(x):
I'm having trouble with this one because x^2 + 4 isn't a perfect square.
--Sue
Hi Sue,
- Csc(x) is 1/sin(x) so
x
csc(x) = x 1/sin(x) = x/sin(x)
Do you know lim[x->0] x/sin(x) ?
- You are correct that x2 + 4 isn't a perfect square but it is positive for all x so you could try g(x) = sqrt(x2 + 4)
Penny