Math Is Fun Forum

mathland

Member

Registered: 2021-03-25

Posts: 444

Find Rate of Change

Find the rate of change of the function at any number c.

f(x) = x^2/(x + 3) as x tends to c.

I need to find the limit of [f(x) - f(c)]/(x - c) as x tends to c.

lim......[(x^2)/(x + 3) - (c^2)/(c + 3)] /(x - c)
x-->c

Stuck here.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Find Rate of Change

hi mathland,

If you can use algebra to get a (x-c) term at the top of that expression, then these can be cancelled out and what's left will allow you to let x tend to c.

Now you can cancel the (x-c) and simplify the rest, put x=c and you're done.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Find Rate of Change

hi mathland,

If you can use algebra to get a (x-c) term at the top of that expression, then these can be cancelled out and what's left will allow you to let x tend to c.

Now you can cancel the (x-c) and simplify the rest, put x=c and you're done.

Bob

Hello Bob. How are you? I took my second vaccine of Moderna yesterday and feel sick today. Everyone told me to expect getting sick the next day. They were right in this respect. I thank for you for using algebra to simplify the original set up.
I can take it from here. No math today. Just not feeling myself. This forum is ok. I would like to see more people involved. It's good to see others participate in the Help Me forum. It's always the same people.

Last edited by mathland (2021-04-11 01:56:52)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Find Rate of Change

Hello mathland,

Sorry he hear you're feeling sick.  Usually it's a sign that your immune system is working so it'll most likely pass quickly.  I had something similar with the astra zenica jab.

Best wishes,

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Find Rate of Change

Hello mathland,

Sorry he hear you're feeling sick.  Usually it's a sign that your immune system is working so it'll most likely pass quickly.  I had something similar with the astra zenica jab.

Best wishes,

Bob

Hello Bob.

How are you? I am feeling better today. It was just the reaction
of the second Moderna vaccine. Now, I can get back to my math studies.