Question

another cal question:
If f is differentiable function such that f(x) is never 0 and int(f(t),t=0..x)=[f(x)]^2 for all x, find f.

Answer 1

\[\int\limits_{0}^{x}f(t) dt=[f(x)]^2\]

Answer 2

that is what that one part says

Answer 3

i need to massage my wrist i will be right back

Answer 4

do you want me to tell you the first thing i would do?

Answer 5

Yes

Answer 6

take derivative of both sides

Answer 7

Differential equations?

Answer 8

yes and we should be able to solve the differential equation pretty easily

Answer 9

\[f(x)=2f(x)f'(x)\]

Answer 10

\[f'(x)=\frac{1}{2}\]

Answer 11

then integrate both sides and then you have f(x)

Answer 12

this problem was too easy
let me see if i find a harder one

Answer 13

so f(x) would be 1/2 x +C ?

Answer 14

yep

Answer 15

:)

Answer 16

so f(t)= 1/2 t right?

Answer 17

\[\int\limits_{0}^{x}(\frac{1}{2}t+C)dt=\frac{1}{2}*\frac{t^2}{2}+Ct+D=\frac{t^2}{4}+Ct+D\]
we want this to be equal to
\[(\frac{1}{2}t+C)^2=\frac{1}{4}t^2+tC+C^2\]
so we need D=C^2

Answer 18

oops just imagine all those t's are x's

Answer 19

where is the D coming from?

Answer 20

its a constant
i added the constant after integrating

Answer 21

you don't need it on a definite integral

Answer 22

oops you are right

Answer 23

imagine there is no D

Answer 24

i think we need to take C to be zero like imaranmeah said

Answer 25

then what about this ...

"f(x) is never 0"

Answer 26

because integral of 1/2 t is t^2 evalatuated from 0 to x
so x^2 but that's not it

Answer 27

what about when x is zero

Answer 28

f(x)=1/2 *x

Answer 29

oh then f would be 0 if x is 0
so this function is wrong

Answer 30

ok so maybe this one is a little harder than i thought

Answer 31

they probably meant to say that f(x) can't be identically zero

Answer 32

do you have the james stewart 6th edition cal book?

Answer 33

the one with big ring on it?

Answer 34

yes

Answer 35

a huge \[\int\limits_{}^{}\] symbol like this is on that cover
yes imranmeah
why is this book so popular?

Answer 36

i don't about this question zarkon
it says never zero

Answer 37

I only have the 7th edition here at home...my 6th edition is in my office

Answer 38

page 345 in my book
who knows you might have the same question

Answer 39

what section

Answer 40

I also have the 7th edition only :/

Answer 41

problem plus after chapter 5

Answer 42

problems plus*

Answer 43

i don't see that problem

Answer 44

number 3

Answer 45

my #3 has stuff with integrals of exponential functions

Answer 46

it sounds like they don't want f(x) to be 0 ever
almost if it were an exponential function or a positive constant

Answer 47

but exponential wouldn't work

Answer 48

the question has no solution as written

since

\[0=\int\limits_{0}^{0}f(t) dt=[f(0)]^2\]

Answer 49

you are right
i don't think they put the answers to the problem plus in the back :(

Answer 50

they dind't want a student to write \[f(x)=0\] as a solution

Answer 51

didn't

Answer 52

they just worded it incorrectly

Answer 53

so maybe they should have said f(x) is not identically zero

Answer 54

like you said

Answer 55

yes...then the above solution... x/2 works

Answer 56

maybe this is why its not in the 7th edition

Answer 57

maybe ;)

Answer 58

thats why joe hates calculus

Answer 59

lol

Answer 60

i hate calculus. >.>

Answer 61

I love calculus :)

Answer 62

joe why you hate cal so much?

Answer 63

i love linear algebra.

Answer 64

doesn't linear algebra use calc?

Answer 65

i guess i should be a little more specific. What i hate in calculus is really just integration. I like everything else.

Answer 66

so you hate integrating something like x^2

Answer 67

no, linear algebra doesnt use calc, its the other way around!
Differentiation is a Linear Transformation on the vector space of functions:

\[\frac{d}{dx}(0) = 0\]
\[\frac{d}{dx}(af(x)+g(x)) = a\frac{d}{dx}f(x)+\frac{d}{dx}g(x)\]

Answer 68

I love calculus, but I see why someone would hate it after being asked to integrate:
\[\int{x^5sin(x)dx}\]Tee hee

Answer 69

the same can be said for integration as well! so there are matrices that represent these transformations. Who needs calc? i'll use the matrix thank you very much :P

Answer 70

i think they should teach remedial linear algebra before algebra
i think easy general things should be thought first

Answer 71

Transformation; is it like jacobian?

Answer 72

taught*
i hat english i swear

Answer 73

hate*

Answer 74

lol

Answer 75

we need to "asianize" americans

Answer 76

@imran yes, the jacobian matrix is also a linear transformation i believe.

Answer 77

Yeah, I hated those; I forgot it during final . Had to cheat from person sitting ahead

Answer 78

you do what you gotta do lol

Answer 79

How in the world can you cheat from the guy in front of you without being seen? xd

Answer 80

the class is on incline. So we are higher than people sitting infront of us

Answer 81

Haha, I bet you pulled a Mr. Bean: http://www.youtube.com/watch?v=98V9cEYe6-A

Answer 82

lol I've seen that,
I did better because no one notice

Answer 83

When I am in library , I think of that Mr.Bean scene