Recent questions in Linear Approximation

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Jonalito Juan2023-05-12

- A body falls from rest against resistance proportional to the square root of the speed at any instant. If the body attains speed V1 and V2 feet per second, after 1 and 2 seconds in motion, respectively, find an expression for the limiting velocity.

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Ghillardi4Pi 2022-11-24

Сalculate which equation represents a line that passes through $(5,1)$ and has a slope of StartFraction one-half EndFraction?

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Tiffany Page 2022-11-13

The third-degree McLauren series approximation for the function $f(x)=\mathrm{ln}(1+x)$ is

$a)x-\frac{1}{24}{x}^{2}+\frac{1}{120}{x}^{3}\phantom{\rule{0ex}{0ex}}b)1-x+\frac{1}{2}{x}^{2}-\frac{1}{6}{x}^{3}\phantom{\rule{0ex}{0ex}}c)x-\frac{1}{2}{x}^{2}+\frac{1}{3}{x}^{3}\phantom{\rule{0ex}{0ex}}d)1-x+{x}^{2}-{x}^{3}\phantom{\rule{0ex}{0ex}}e)x-{x}^{2}+{x}^{3}$

$a)x-\frac{1}{24}{x}^{2}+\frac{1}{120}{x}^{3}\phantom{\rule{0ex}{0ex}}b)1-x+\frac{1}{2}{x}^{2}-\frac{1}{6}{x}^{3}\phantom{\rule{0ex}{0ex}}c)x-\frac{1}{2}{x}^{2}+\frac{1}{3}{x}^{3}\phantom{\rule{0ex}{0ex}}d)1-x+{x}^{2}-{x}^{3}\phantom{\rule{0ex}{0ex}}e)x-{x}^{2}+{x}^{3}$

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Yair Valentine 2022-08-07

A carousel has a radius of 17 ft and takes 28 seconds to make one complete revolution. What is the linear speed of the carousel at its outside edge?

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Meossi91 2022-08-03

Earth rotates on an axis through its poles. The distance from the axis to a location on Earth 40 degrees north latitude is about 3033.5 miles. Therefore, a location on Earth at 40 degrees north latitude is spinning on a circle of radius 3033.5 miles. Compute the linear speed on the surfuce of Earth at 40 degrees north latitude.

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Waldronjw 2022-07-15

Let $y=f(x)=({x}_{1}^{2}+2{x}_{2},{x}_{1}{x}_{2}-3{x}_{1})$

Is the linear approximation just $f(y)=f(x)+A(y-x)$ whenever y is approximately near $x$?

Is the linear approximation just $f(y)=f(x)+A(y-x)$ whenever y is approximately near $x$?

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Riya Hansen 2022-07-12

Linear approximation of quotient

$\frac{(2.01{)}^{2}}{\sqrt{.95}}$

$\frac{(2.01{)}^{2}}{\sqrt{.95}}$

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nidantasnu 2022-07-12

Use a linear approximation to estimate the number ${8.07}^{2/3}$

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orlovskihmw 2022-07-11

If $f(x)=g(x)h(x)$

does the linear approximation of $f(x)$ equals the linear approximation of $g(x)$ times the linear approximation of $h(x)$?

is it true for quadratic approximations as well?

does the linear approximation of $f(x)$ equals the linear approximation of $g(x)$ times the linear approximation of $h(x)$?

is it true for quadratic approximations as well?

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ziphumulegn 2022-07-09

Since we know that in a good linear approximation, $L(x)=f(a)+{f}^{\prime}(a)(x-a).$. But what if ${f}^{\prime}(a)$ does not exist? How to prove that if a function has a good linear approximation, then it must be differentiable?

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Davon Irwin 2022-07-01

If a line is a linear approximation to a function in $1$ variable and a hyperplane is the linear approximation to a function in $2$ variables what is the linear approximation to a function in $3$ variables?

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Reginald Delacruz 2022-06-27

The volume $V$ of a cylinder is computed using the values 6m for the diameter and $9.8$m for the height. Use the linear approximation to estimate the maximum error in $V$ if each of these values has a possible error of at most $7$%.

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kokoszzm 2022-06-24

The function $g$ is defined by $g(x)={\int}_{-20}^{x}(f(t){)}^{2}dt,$, and we're given

$g(20)=100,f(0)=4,{f}^{\prime}(0)=12,{f}^{\u2033}(0)=20.$

use a tangent line approximation to estimate $g(0.1)$

$g(20)=100,f(0)=4,{f}^{\prime}(0)=12,{f}^{\u2033}(0)=20.$

use a tangent line approximation to estimate $g(0.1)$

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gnatopoditw 2022-06-24

$f(x,y)=\surd (7+2xy)$Find the linear approximation at $(3,-1)$

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Mohammad Cannon 2022-06-15

Proceed estimating this quantity using Linear Approximation

$\frac{1}{\sqrt{95}}}-{\displaystyle \frac{1}{\sqrt{99}}$

$\frac{1}{\sqrt{95}}}-{\displaystyle \frac{1}{\sqrt{99}}$

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Petrovcic2x 2022-06-13

Find the linear approximation of the function

$f(x,y)=\mathrm{ln}(e+x+y)$

at point $(0,0)$. Use it to approximate the value of the function at $(0.1,0.2)$

$f(x,y)=\mathrm{ln}(e+x+y)$

at point $(0,0)$. Use it to approximate the value of the function at $(0.1,0.2)$

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Yesenia Sherman 2022-06-12

Use Linear Approximation to estimate $\mathrm{\Delta}f=f(3.02)-f(3)$

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Jeffery Clements 2022-06-12

Linear approximation by rational number to $4\sqrt{3}$

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Celia Lucas 2022-06-08

Use a linear approximation of

$f(x)=\sqrt[3]{x}$

at

$x=8$

to approximate

$\sqrt[3]{7}$

Express your answer as an exact fraction.

$f(x)=\sqrt[3]{x}$

at

$x=8$

to approximate

$\sqrt[3]{7}$

Express your answer as an exact fraction.

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opepayflarpws 2022-06-06

You're measuring the velocity of an object by measuring that it takes $1$ second to travel $1.2$ meters. The measurement error is $001$ meters in distance and the error in time is $01$ second.

What is the absolute value of the error in the linear approximation for the velocity?

What is the absolute value of the error in the linear approximation for the velocity?

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The majority of college students that seek linear approximation practice problems with answers do not really know the concept of linear approximation when using basic differential equations. The trick is to use an approximation of a general function by turning to an affine function. When you need to work with an approximation for analytical work, focus on the solutions that provide linear approximation questions and answers where you see certain relations. It is good to compare several similar answers as it may help you come up with calculations and the explanation of your approximates with the graphs and the formulas.