Lagrange remainder vs. Alternating Series Estimation Theorem: do they always provide the same error bound? If a function has a nth degree Taylor series approximation, we can use the Lagrange form of the remainder to calculate the maximum value of the error of approximation. If the series is also an alternating series, we can use the Alternating Series Estimation Theorem to get another maximum value of the error of approximation. It is not guaranteed that the two maximums will always be the same.

What is the derivative of the work function?

How to use implicit differentiation to find ${\displaystyle \frac{dy}{dx}}$ given ${\displaystyle 3x^2+3y^2=2}$?

How to differentiate $y=\log <!--\; \; -->x^2$?

The solution of a differential equation y′′+3y′+2y=0 is of the form
A) $c_1{e}^x+c_2{e}^{2x}$
B) $c_1{e}^{-<!--\; -\; -->x}+c_2{e}^{3x}$
C) $c_1{e}^{-<!--\; -\; -->x}+c_2{e}^{-<!--\; -\; -->2x}$
D) $c_1{e}^{-<!--\; -\; -->2x}+c_2{2}^{-<!--\; -\; -->x}$

How to find instantaneous velocity from a position vs. time graph?

How to implicitly differentiate ${\displaystyle \sqrt{xy}=x-2y}$?

What is 2xy differentiated implicitly?

How to find the sum of the infinite geometric series given ${\displaystyle 1+\frac{2}{3}+\frac{4}{9}+...}$?

Look at this series: 1.5, 2.3, 3.1, 3.9, ... What number should come next?
A. 4.2
B. 4.4
C. 4.7
D. 5.1

What is the derivative of ${\displaystyle \frac{x+1}{y}}$?

How to find the sum of the infinite geometric series 0.9 + 0.09 + 0.009 +…?

How to find the volume of a cone using an integral?

What is the surface area of the solid created by revolving ${\displaystyle f\left(x\right)=e^{2-x},x\in [1,2]}$ around the x axis?

How to differentiate ${\displaystyle x^{\frac{2}{3}}+y^{\frac{2}{3}}=4}$?

The differential coefficient of $\sec \left({\tan }^{-1}\left(x\right)\right)$.