Question

extimate using the Linear Approximation and find the error using a calculator. $\frac{1}{(27.5)^{5 / 3}}-\frac{1}{243}$ 

   extimate using the Linear Approximation and find the error using a calculator.
 $\frac{1}{(27.5)^{5 / 3}}-\frac{1}{243}$
Calculus
Calculus
Jon Rogawski,… 2nd Edition
Chapter 4, Problem 22 ↓
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extimate using the Linear Approximation and find the error using a calculator. $\frac{1}{(27.5)^{5 / 3}}-\frac{1}{243}$
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00:01 Using linearization is a calculator to compute the percentage error and so we're given 1 .2 to the 5 thirds so in order to find the linearization we can use this equation here as given from the textbook um so we can set f of x equal to x to the 5 thirds um and a equal to 1 so now we want to find the derivative of f of x so we can use the power down rule here where we bring down the power of five -thirds and leaving us with x to the two -thirds and since we want to find the derivative at the point a we will plug in one into the derivative and since we know one to any power equals one this this leaves us with 5 thirds as the derivative.
01:31 So now we can plug in everything into the linearization equation.
01:37 So we have l of x is equal to 5 thirds times x minus 1 plus 1, which we obtained by plugging in a equals 1 into the original ffx equation...
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