# Calc 1 HW help needed.

• Apr 22nd 2007, 07:38 PM
lmao
Calc 1 HW help needed.
1. The linear approximation at x=0 sqrt(5+7x) A+Bx
where A=_____
and B=_____

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2. The linear approximation at x=0 to sin(9x) is A+Bx where A is : and where B is:

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3.The linear approximation at x=0 to 1/sqrt(7x) is A+Bx where A is: and where B is:

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4. Find the linear approximation of f(x)=lnx at x=1 and use it to estimate ln1https://webwork.math.uga.edu/webwork...144/char3A.png1.
L(x)=

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5.The circumference of a sphere was measured to be 90https://webwork.math.uga.edu/webwork...144/char3A.png000 cm with a possible error of 0https://webwork.math.uga.edu/webwork...144/char3A.png50000 cm. Use linear approximation to estimate the maximum error in the calculated surface area. Estimate the relative error in the calculated surface area.
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6. You have a sphere and you want to know its diameter and volume, but you have no calipers handy. You do have a tape measure, however. You wrap the tape measure around the sphere and measure 14 inches. What with the difficulties of measuring around a sphere and reading the measure, you figure that you are within 81 inch of the true measure. Using these numbers and linear approximation (as you did in the first few problems of this assignment), you estimate the diameter of the sphere to be at least but not more than inches and its volume to be at least but not more than cubic inches.
Answers must be correct to 4 decimal places.

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7.A beam of thickness t sags by 8/(t^2) inches when a certain weight is hung from its middle. The sag can be figured into the construction plans only if its value is known to within 0.07 inches. How accurately must the thickness of the beam be measured to achieve this tolerance for a beam which is essentially 4.8 inches thick? Measurement Tolerance: https://webwork.math.uga.edu/webwork...144/char06.pngin

I have done the majority of the HW, but these are the ones I cannot do. This is due at 1AM so any help is appreciated!
• Apr 23rd 2007, 04:48 AM
topsquark
Quote:

Originally Posted by lmao
1. The linear approximation at x=0 sqrt(5+7x) A+Bx
where A=_____
and B=_____

Use the Taylor's series.

f(x) = sqrt{5 + 7x} where x is small (ie. near 0).

f(0) = sqrt{5}

f'(x) = 7/(2*sqrt{5 + 7x}), so f'(0) = 7/(2*sqrt{5})

Thus
f(x) (approx) sqrt{5} + [7/(2*sqrt{5})]*x

-Dan