On my last test I got four problems wrong. I'd like to know what I did wrong on these for my final.(adsbygoogle = window.adsbygoogle || []).push({});

1. Given f(x) = x^(3/2) ; x=4; and delta x = dx = 0.1; calculate delta y

2. Use differentials to approximate the change in f(x) if x changes from 3 to 3.01 and f(x) = (3x^2-26)^10

3. f(x) = x^(-1/3); approximate (7.952)^(-1/3)

4. The equatorial radius of the earth is approx 3690 miles. Suppose a wire is wrapped tightly around the earth at its equator. How much must this wire be lengthened if it is to be strung on poles 10 feet above the ground.

My solutions

1.

delta y = f(x+ delta x) - f(x) = 4.1^(3/2) - 0.1^(3/2)

2.

f'(x)dx = 10(1)^9 times 0.01 = 0.1

3.

f(8) - f'(8)(0.048) = 1/2 - (-1/3)(8^(-4/3))(0.048) = 1/2 - (1/48)(0.048) = 1/2 - 0.001 = 499/1000

4.

f'(x)dx

f(x)=2 pi r

f'(x) = 2 pi

f'(x)dx = 2 pi times 10 = 20 pi

If you could help me with even one of the problems, I'll be happy. I think I might be making the same time of mistake, since the problems are so similar.

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# Homework Help: Four Problems on Linear Approximation

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