Question

Find the linear approximation of the function f(x) = \sqrt{1-x} at a = 0 and use it to approximate the numbers \sqrt{0.9} and \sqrt{0.99}. (Round your answers to four decimal places.) L(x) = \sqrt{0.9} \approx \sqrt{0.99} \approx

Differential equations
ANSWERED
asked 2021-05-03
Find the linear approximation of the function \(f(x) = \sqrt{1-x}\) at a = 0 and use it to approximate the numbers \(\sqrt{0.9}\) and \(\sqrt{0.99}\). (Round your answers to four decimal places.)
L(x) =
\(\sqrt{0.9} \approx\)
\(\sqrt{0.99} \approx\)

Expert Answers (1)

2021-05-04

\(f(x) = \sqrt{1 - x}\)
f(0) = 1
pt (0,1)
\(f'(x) = \frac{1}{2} \cdot (1-x)^{-\frac{1}{2}} \cdot -1\)
\(f'(x) = (-\frac{1}{2}) \cdot (x-1)^{-\frac{1}{2}}\)
\(T(x) = 1 - \frac{1}{2} \cdot (x)\)
To estimate 0.9 we need to put in 0.1 and 0.01\(T(0.1) = 1 - \frac{1}{2} \cdot 0.1 = 1 - 0.05 = 0.95\) \(T(0.01) = 1 - \frac{1}{2} \cdot 0.01 = 0.995\)

13
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours

Relevant Questions

asked 2021-06-01

Find the linear approximation of the function \(f(x)=\sqrt{4-x}\) at \(a=0\)
Use L(x) to approximate the numbers \(\sqrt{3.9}\) and \(\sqrt{3.99}\) Round to four decimal places

asked 2021-06-11

Find the linear approximation of the function \(f(x)=\sqrt{1-x}\) at \(a=0\) and use it to approximate the numbers \(\sqrt{0.9}\) and \(\sqrt{0.99}\).

asked 2021-05-14
Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.
\(\begin{array}{|c|c|}\hline 11.8 & 7.7 & 6.5 & 6 .8& 9.7 & 6.8 & 7.3 \\ \hline 7.9 & 9.7 & 8.7 & 8.1 & 8.5 & 6.3 & 7.0 \\ \hline 7.3 & 7.4 & 5.3 & 9.0 & 8.1 & 11.3 & 6.3 \\ \hline 7.2 & 7.7 & 7.8 & 11.6 & 10.7 & 7.0 \\ \hline \end{array}\)
a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. \([Hint.\ ?x_{j}=219.5.]\) (Round your answer to three decimal places.)
MPa
State which estimator you used.
\(x\)
\(p?\)
\(\frac{s}{x}\)
\(s\)
\(\tilde{\chi}\)
b) Calculate a point estimate of the strength value that separates the weakest \(50\%\) of all such beams from the strongest \(50\%\).
MPa
State which estimator you used.
\(s\)
\(x\)
\(p?\)
\(\tilde{\chi}\)
\(\frac{s}{x}\)
c) Calculate a point estimate of the population standard deviation ?. \([Hint:\ ?x_{i}2 = 1859.53.]\) (Round your answer to three decimal places.)
MPa
Interpret this point estimate.
This estimate describes the linearity of the data.
This estimate describes the bias of the data.
This estimate describes the spread of the data.
This estimate describes the center of the data.
Which estimator did you use?
\(\tilde{\chi}\)
\(x\)
\(s\)
\(\frac{s}{x}\)
\(p?\)
d) Calculate a point estimate of the proportion of all such beams whose flexural strength exceeds 10 MPa. [Hint: Think of an observation as a "success" if it exceeds 10.] (Round your answer to three decimal places.)
e) Calculate a point estimate of the population coefficient of variation \(\frac{?}{?}\). (Round your answer to four decimal places.)
State which estimator you used.
\(p?\)
\(\tilde{\chi}\)
\(s\)
\(\frac{s}{x}\)
\(x\)
asked 2021-05-09
Find the linear approximation of the function \(g(x)=(1+x)^{\frac{1}{3}}\) at a=0 and use it to approximate the numbers \((0.95)^{\frac{1}{3}}\) and \((1.1)^{\frac{1}{3}}\).
...