Estimating (16.1)1/4 using Taylor's Expansion at x=16

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Homework Statement



Use the taylor's expansion of f(x)= x1/4 about x= 16 to estimate (16.1)1/4

Homework Equations


Taylors formula: f(a) + f'(a) (x-a) + (f''(a)/2!) (x-a)2+...

The Attempt at a Solution



Ok I have calculate the taylor expansion to be: 2 + (1/32) (x-16)-(3/320) (x-16)2+ (7/262144) (x-16)3

I just don't know what to do after this - do i just substitute 16.1 into the value for x in the taylor expansion I have just found?
 
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yep - then check whether you're close with a caclulator
 
thanks it works
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

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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