To estimate the given number using linear approximation, we can use the function f(x) = √x. We know that √100 = 10, so we can use 100 as our "a" value, and 100.4 as our "x" value.

The formula for linear approximation is L(x) = f(a) + f'(a)(x - a).

First, we need to find the derivative of f(x) = √x. Using the power rule, the derivative f'(x) = 1/(2√x).

Substituting a = 100 into the derivative, we get f'(100) = 1/(2√100) = 1/20.

Now we can substitute a = 100, x = 100.4, f(a) = 10, and f'(a) = 1/20 into the linear approximation formula:

L(100.4) = 10 + (1/20)(100.4 - 100) = 10 + (1/20)(0.4) = 10 + 0.02 = 10.02.

So, the linear approximation of √100.4 is approximately 10.02.

Question

To estimate the given number using linear approximation, we can use the function f(x) = √x. We know that √100 = 10, so we can use 100 as our "a" value, and 100.4 as our "x" value.

The formula for linear approximation is L(x) = f(a) + f'(a)(x - a).

First, we need to find the derivative of f(x) = √x. Using the power rule, the derivative f'(x) = 1/(2√x).

Substituting a = 100 into the derivative, we get f'(100) = 1/(2√100) = 1/20.

Now we can substitute a = 100, x = 100.4, f(a) = 10, and f'(a) = 1/20 into the linear approximation formula:

L(100.4) = 10 + (1/20)(100.4 - 100) = 10 + (1/20)(0.4) = 10 + 0.02 = 10.02.

So, the linear approximation of √100.4 is approximately 10.02.

Knowee AI · Accepted Answer

To estimate the given number using linear approximation, we can use the function f(x) = √x. We know that √100 = 10, so we can use 100 as our "a" value, and 100.4 as our "x" value.

The formula for linear approximation is L(x) = f(a) + f'(a)(x - a).

First, we need to find the derivative of f(x) = √x. Using the power rule, the derivative f'(x) = 1/(2√x).

Substituting a = 100 into the derivative, we get f'(100) = 1/(2√100) = 1/20.

Now we can substitute a = 100, x = 100.4, f(a) = 10, and f'(a) = 1/20 into the linear approximation formula:

L(100.4) = 10 + (1/20)(100.4 - 100) = 10 + (1/20)(0.4) = 10 + 0.02 = 10.02.

So, the linear approximation of √100.4 is approximately 10.02.

Use a linear approximation (or differentials) to estimate the given number.100.4

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