Give an example of a function g(x) and a function h(x) with the following properties?

[melinlala]

[h=1]lim g(x)=0
x->7

lim h(x)=0
x->7

lim [g(x)]^2/h(x) = 2
x->7[/h]
I simply do not understand the question? What does it want? Please help me!!!

 

[stapel]

\(\displaystyle \displaystyle \lim_{x\, \rightarrow\, 7}\, g(x)\, =\, 0\)

\(\displaystyle \displaystyle \lim_{x\, \rightarrow\, 7}\, h(x)\, =\, 0\)

\(\displaystyle \displaystyle \lim_{x\, \rightarrow\, 7}\, \dfrac{\left[ g(x) \right]^2}{h(x)}\, =\, 2\)

I simply do not understand the question? What does it want?

There is no actual question within your post. Are you perhaps referring to the subject line? Is that the rest of the post, containing the instructions?

If so, then they're asking you to figure out two functions (your choice) that happen to have the listed properties. Have you studied limits at all?

If not, please reply with clarification. Thank you!

 

[Deleted member 4993]

lim g(x)=0
x->7

lim h(x)=0
x->7

lim [g(x)]^2/h(x) = 2
x->7


I simply do not understand the question? What does it want? Please help me!!!

What if you had:

h(x) = (x-7)² and

g(x) = (x-7)

What would be

lim [g(x)]^2/h(x) = ??
x->7

 

[pka]

What if you had:
h(x) = (x-7)² and g(x) = (x-7)
What would be
lim [g(x)]^2/h(x) = ??
x->7

May I suggest \(\displaystyle g(x)=\sqrt2(x-7)\)?