# Limits questions

1. Sep 26, 2008

### aleferesco

1) If the limit of the function g(x) = [f(x) -8]/[x-1] is equals to 10 as x approches 1, then find the limit of f(x) as x approaches 1

2) If the limit of the function h(x) = f(x)/x2 is equals to 5 as x approaches 0, then find the following limits

a) limit of f(x) as x approaches zero

b) limit of f(x)/x as x approaches zero

---> Attempt answer for question number 1

..so what I understand from the two questions is that they don't really require much calculations, These only require the understanding of whats happening to the original limits. I know that in the first question the fact that they are tellings us that there is a limit for g(x) helps us determine that there has to be also a limit for f(x) since it is part of the g(x). So basically I know that f(x) has to be at least 8 so that when I substitute the x=1 values into g(x), it will give me an indeterminate number (0/0)

so for some reason the answer to this question is: the limit of of f(x) is equals to 8 as x approaches 1 (does the explanation that I made supports this answer, if not please help)

---> Attempt answer for question number 2

ps. If you are confused by my attempted explanation to question number 1, please let me know or explain it to me in the way that you understand it

ps2. Sorry that I gave an verbal representation for the questions instead of writting the equations out (I'm new in this forum)

thanks
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Sep 26, 2008

### gabbagabbahey

I think to properly solve the first question you need to exploit some of the properties of limits.
For example, if the limits as x->c of u(x) and v(x) exist and are finite, the following hold true:

$$\lim_{x \to c} u(x)v(x)= \left( \lim_{x \to c} u(x) \right) \left( \lim_{x \to c} v(x) \right)$$

and

$$\lim_{x \to c} (u(x)-v(x))= \left( \lim_{x \to c} u(x) \right) - \left( \lim_{x \to c} v(x) \right)$$

3. Sep 26, 2008

### Dick

You have the right idea. Sure lim x->0 f(x)=8, in the first case. If the limit were not 8 then the limit of the quotient would not exist. Apply the same reasoning to the second. x^2->0. What must f(x) approach? 1/x goes to infinity. What must f(x)/x approach?