Approximating Square Roots with Linear Approximation

thushanthan
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Homework Statement



Given f(x)=sqrt(2x+2)

Question : Find the linear approximation of f(x) at a=7 AND use it to approximate sqrt(18).


Homework Equations



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

The Attempt at a Solution



Using the linear approximation formula I am getting the value 6.75, but when I checked with calculator the value of sqrt(18) is 4.2426...

Did my approximation is wrong?
 
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Yes, you did something wrong. Show us your work. It's kinda hard to tell where you went wrong without that.
 
Thank you :smile:

I didn't solve 2x+2=18. I plugged in x=18 and (x-a) becomes (18-7) = 11.

Now I got it. Thanks.
 

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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