really a great thanksby moham_87 Tags: None 

#1
Jan804, 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)<=uv * 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 



#2
Jan804, 06:38 PM

P: 640

loll... how old are you kid? 



#3
Jan904, 05:52 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,881

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))/(ba)." 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+h^{2})^{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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