Quandaries and Queries


Who is asking: Student
Level: Secondary

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.




Hi Sue,

  1. 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) ?

  2. 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)



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