# Thread: Limit of a function

1. ## Limit of a function

Some questions concerning limits.

How do I sketch a graph when I'm given limit info, for example this
lim f =2(as x approaches 0^-)
lim f =0(as x approaches 4^+)
lim f =0(as x approaches 0^+)
lim f =3 ( as x approaches 4^-)
f(0)=2
f(4)=1

I have some vague idea how to do it, but my sketches do not seem like graphs.

Prove that lim sqrt(x)*e^(sin(pi:x)) =0(as x approaches 0^+)
no idea where to start this, I could graph is on graphing calculator but that is worthless, i cannot use limit laws as e^sin(pi/x) doesnt exist as you cant divide by zero.

Suppose that
x^4<f(x)<x^2
if |X|<1 and
x^2<f(x)<x^4
if |x|>1
find value of limits
lim f(x) as x approaches -1
lim f(x) as x approaches 0
lim f(x) as x approaches 1

Last one I just wanna make sure I did right,
is there a number c such that
lim ((2x^2+cx-4c)/(x^2+x-6)) (as x approaches 2) exists?
If so find value of c and calculate limit
what i did is a bit of guessing
factor x^2+x-6
x^2+x-6=(x-2)(x+3)
now this is where guessing comes in
2x^2+cx-4c.
D=c^2+32c
so D must be a sqrt of something otherwise i cant see it being factored
let c=4 then D=144 then
2x^2+cx-4c=2x^2+4x-16=(x+4)(x-2)
x-2 is canceled, therefore
(x+4)/(x+3)
rest is obvious.
Forgive me for my wall of text and my poor understanding of math, any help is appreciated!

2. ## Re: Limit of a function

I wonder if anyone can read this post?
It is totally unreadable as far as I can see.