Linearization of ln(7x) at a=1/7

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Homework Statement


find the linearization of L(x) at a.
f(x)=ln7x, a=1/7


Homework Equations


f(a)+f'(a)(x-a)


The Attempt at a Solution



i got f(1/7)=0 and f'(1/7)=9.12
then shouldn't it be 0+.9.12(x-0)=9.12x?
 
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Not quite - Check your derivative again - if it helps, remember, ln(ax) = ln(a) + ln(x).
 

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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