Approximating Square Roots with Linear Approximation

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The discussion revolves around finding the linear approximation of the function f(x) = sqrt(2x + 2) at a = 7 to estimate sqrt(18). The user initially calculated an approximation of 6.75 but realized it was incorrect after comparing it with the actual value of sqrt(18), which is approximately 4.2426. The error was identified as not properly solving for x in the equation 2x + 2 = 18 and incorrectly substituting x = 18 instead. After clarifying the steps, the user corrected their approach and understood the mistake. The thread highlights the importance of correctly applying the linear approximation formula and solving equations accurately.
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.
 

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