For questions about linear approximations, $f(x) \approx f(a)+f'(a)(x-a)$ for $x$ around $a$.
Questions tagged [linear-approximation]
264 questions
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Linear Approximation and Volume of Cylinder
I was given the question:
The volume V of a cylinder is computed using the values 6m for the diameter and 9.8m 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…
Neil H
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How can I use the differencial to approximate a function with a tangent plane?
Problem (translating from Spanish as exactly as I can, so please bear with me): Knowing that $f(x,y)$ is differentiable in $(5; -3)$ which is inside the function domain, and that $\frac{\partial f}{\partial x}(5;-3)=2$ and $\frac{\partial…
Floella
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Log linear approximation
I was reading on Likelihood ratio text, and I found an example wit Bernouli trials, along the simplification they did this:
Click to view Image
I cant figure out how they did that. I don't want the direct answer, hints are enough.
Toney Shields
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percentage decrease of the edge of an icecube
I have a question that is asking to find an approximation for the percentage the the edge length of an ice cube will decrease if the cube loses six percent of its volume. The question instructs us to use differential (linear) approximation
My maths…
Lincoln77
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$f(x) = e^x$ and $a = 1$. Find the linear approximation $L(x)$
I a little confused on this question and I feel I shouldn't be. So, I take the derivative of f(x) which is $f'(x)=e^x$
Next I plug in the point $a = 1$, which then gives me the slope $2.71$
Knowing $L(x)= f'(a)(x-a)+ f(a)$
I plug $f(1)$ into the…
user3339882
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Basic Linear Approximation
I have come across the need to quickly perform linear approximations, for example I ran across this simplification provided r << d (I think maybe it should be r >> d).
$2(r + d)^{-2} - r^{-2} - (r + 2d)^{-2} = 2 - \frac{2d}{r} - 1 - 1 +…
user7348
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Differentials to find approximate values
I'm asked to solve the following without a calculator:
$80^{3/4}$
I only know that $f(x+dx) \approx f(x) + dy$
I then proceed to find $dy$, it should follow that if $f(x) = x^{3/4}$, then $dy = \dfrac{3}{4\sqrt[4]{x}}dx$.
The issue I have at this…
complexguest
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