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Really a great thanks

by moham_87
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moham_87
#1
Jan8-04, 05:29 PM
P: 13
again, i've another question i wish it is the last.
it is about "Mean Value Theorem",

* if u and v are any real numbers, then, prove that:
|sin(u)-sin(v)|<=|u-v|

* Prove that [(1+h)^(1/2)] < [1+(h/2)], for h>0

* Suppose that f'(x)=g'(x)+x for every (x) in some interval (I), how different can the function (f) and (g) be

I don't know from where to start and i would like you to know that i'm in exams' days, and that's not assignment

thank you alot for your efforts
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PrudensOptimus
#2
Jan8-04, 06:38 PM
P: 640
Originally posted by moham_87
again, i've another question i wish it is the last.
it is about "Mean Value Theorem",

* if u and v are any real numbers, then, prove that:
|sin(u)-sin(v)|<=|u-v|

* Prove that [(1+h)^(1/2)] < [1+(h/2)], for h>0

* Suppose that f'(x)=g'(x)+x for every (x) in some interval (I), how different can the function (f) and (g) be

I don't know from where to start and i would like you to know that i'm in exams' days, and that's not assignment

thank you alot for your efforts

loll... how old are you kid?
HallsofIvy
#3
Jan9-04, 05:52 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,363
Prudens Optimus, why "lol"? These seem like reasonable questions to me.

moham_87, since you say that these are about the "mean value theorem", how about using that?

Mean Value Theorem: "If f is continuous on [a,b] and differentiable on (a,b) then there exist c in [a,b] such that
f'(c)= (f(b)- f(a))/(b-a)."

In the first problem, f(x)= sin(x). What is f'(x)? What is the largest possible value of f'(x)?

In the second problem, f(x)= (1+h2)1/2. What is f'(x)? What is the largest possible value of f'(x)?

In the third problem, if f'(x)=g'(x)+x , what is f(x)?


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