Math Is Fun Forum

Kurtz

Member

Registered: 2007-10-01

Posts: 27

Need Help!!!

How do I find the Limit for a function F(x)= -3x +2

Book studying isn't going too well

---

I am a mathemagician. You ask why? I point up

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Need Help!!!

Is that the whole question? (to me at least) that doesn't make much sense.

Kurtz

Member

Registered: 2007-10-01

Posts: 27

Re: Need Help!!!

Unfortunately yes it is thats why I'm pretty confused because this how its asked.

Limits and Funtions

For each function, find       lim     f(x+Δx)-f(x)
                                   Δx->0    --------------
                                                       Δx

1. f(x)= -3x + 2

2. f(x)= x^2

             and so on.....

---

I am a mathemagician. You ask why? I point up

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Need Help!!!

Well I wanted what x tended to! So in other words it wants you to differentiate from 'first principles'. How far have you got?

You can look below and apply the same steps to the other questions.

Last edited by Daniel123 (2008-08-08 19:03:34)

Kurtz

Member

Registered: 2007-10-01

Posts: 27

Re: Need Help!!!

So we're practically subtracting "f" by one time so like

f(x)= X^2 + 14
               will end up with
                                      lim x      because everything else would be cancelled right?

---

I am a mathemagician. You ask why? I point up

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Need Help!!!

It sometimes gets more complicated than the one Daniel did, so you can't assume things like that.
f(x) = x² + 14 would be differentiated like this:

---

Why did the vector cross the road?
It wanted to be normal.

MooseofDoom

Member

Registered: 2008-08-10

Posts: 13

Re: Need Help!!!

Hey Kurtz, how do you do it?

---

π≈ 3.141 592 653 589 793 238 462 643 383 279 502 884 197 169 399 375 105 820 974 944 592 307 816 406 286 208 998 628 034 825 342 117 067 982 148 086 513 282 306 647 093 844 609 550 582 231 725 359 408 128 481 117 450 284 102 701 938 521 105 559 644 622 948 954 930...

Kurtz

Member

Registered: 2007-10-01

Posts: 27

Re: Need Help!!!

Have you check the "hidden text" given by Daniel and Maths up on top it should help you its done step by step using the limit formula. Just click on it and study it but then it wont help on all of the problems.

So I have one question how would I solve something such as

        f(x)= -x² - x + 1    and f(x)= √ x

---

I am a mathemagician. You ask why? I point up

MooseofDoom

Member

Registered: 2008-08-10

Posts: 13

Re: Need Help!!!

Doh... Yeah clicking on Hidden Text helps a lot lol.... Thanks

---

π≈ 3.141 592 653 589 793 238 462 643 383 279 502 884 197 169 399 375 105 820 974 944 592 307 816 406 286 208 998 628 034 825 342 117 067 982 148 086 513 282 306 647 093 844 609 550 582 231 725 359 408 128 481 117 450 284 102 701 938 521 105 559 644 622 948 954 930...

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Need Help!!!

f(x) = -x² - x + 1 should be no problem if you understand how I did x² + 14 above.

f(x) = √x is harder though, because it wants you to find:

Unlike the previous examples, √(x+δ) can't be expanded nicely and so it's quite a nasty expression. The function is easy enough to differentiate, but I don't see how to do it from first principles.

---

Why did the vector cross the road?
It wanted to be normal.

makar92

Member

Registered: 2008-08-10

Posts: 6

Re: Need Help!!!

deriving from the derive definition of f(x)=√x you do like this:

(f(x+h)-f(x)/h) = √(x+h)-√(x)/h, then you multiply with (√(x+h)-√(x)) making it all (√(x+h)+√(x))*(√(x+h)-√(x)) / h*(√(x+h)+√(x)) = (x+h-x) / (h*(√(x+h)+√(x))) = 1 / (√(x+h)+√(x)).

then we make h go towards zero.

f'(x)=lim_h-->0(1/(√(x+h)+√(x)) = 1 / (√(x) + √(x)) = 1 / 2*√(x)

f(x)=√(x) gives f'(x)= (1/(2√(x)))

Last edited by makar92 (2008-08-11 03:00:46)

Kurtz

Member

Registered: 2007-10-01

Posts: 27

Re: Need Help!!!

by using the variable "h" you are referring to {\delta} right?

Last edited by Kurtz (2008-08-11 10:05:39)

---

I am a mathemagician. You ask why? I point up

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Need Help!!!

Yeah, it doesn't matter what variable is used for the limit. I used delta because Daniel already did, but h is used commonly as well.

---

Why did the vector cross the road?
It wanted to be normal.

devindranath

Member

Registered: 2008-08-21

Posts: 1

Re: Need Help!!!

How do I find the Limit for a function F(x)= -3x +2

Book studying isn't going too well

i'll have to agree with daniel

devindranath

Member

Registered: 2008-08-21

Posts: 1

Re: Need Help!!!

how do i explain BODMAS?:{