Solve 5 Problems: Get Help Now!

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What are you having problems with. You have to show some work for each of the problems before getting any help here.
 
Ok for question 2 i need to see if in part A if it statisfys the Mean Value Theorem, and if it does which is the value of C which statistfies the condition of the theorem

f(x)=(16-x^2)^1/2 on [-4,4]

if differentiate it should like this or i am not smart

-x/(16-x^2)^1/2

From the looks of it it does not but i just want to see anyone elses opinion
 
Your differentiation is OK, now you need to find a point c in (-4,4) which satisfies:

f'(c)=\frac{f(4)-f(-4)}{4-(-4)}
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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