Homework Statement
My apologies in advance for the messiness of the equations; the computers available to us do not correctly process the LaTex code.
I am tasked with estimating the area under the curve f(x)=x2+1 on the interval [0,2] using 16 partitions. Online calculators and my...
Homework Statement
I am to explain all intercepts, critical numbers, extrema, inflection points, and asymptotes of the function f(x)=(x-4)/x^3.
2. The attempt at a solution
a) The y-intercept does not exist, as the domain of the function is all real numbers except x=0. Solving the...
The first part seems to be a contradiction because it asks you if you can think of any functions with a derivative equal to 2x, and then lists two examples. It then goes on to ask if there are any other functions with the derivative 2x (after it just gave us three) and says there are none...
There are a number of different ways to enter the problem to achieve the intended result. I have tried a few variations, all with the same results.
(2*((-2)^3))-(3*((-2)^2))=-4
(2*((z)^3))-(3*((z)^2))=-28
This is a piece of the derivative of a function, and -2 is one of the zeros of the...
I was working with a much longer equation and receiving a result I didn't expect, and finally narrowed it down to the following section:
2(-2^3)-3(-2^2)
2(-2^3) is correctly calculated as -16 independently, and 3(-2^2) is correctly calculated as 12 (again, independently) for a difference...
I've hit a snag in my studies, namely something my book labels "Corollary 10.1":
[i]Are there any other functions with the same derivative as x^2+2=2x? You should quickly come up with several: x^2+3 and [itex x^2-4[/itex] for instance. In fact, d/dx[x^2+c]=2x for any constant c. Are there...
I set d/dt[h] = 1 because I understand the power rule to state that a variable with no exponent (or more correctly, an exponent of 1) to differentiate to 1 (h^1 = 1h^0 = 1(1) = 1). Are you suggesting I convert h to terms of r prior to differentiation?
A) V = 1/3(π)(r^2)(h)
1. dV/dt =...
Homework Statement
I've worked through both parts of this question twice in what I assume is the correct manner, but I'm receiving an unexpected result from part B. The question is as follows:
Sand is dumped such that the shape of the sandpile remains a cone with height equal to twice...
Homework Statement
I am struggling with implicit derivatives, and though my course book includes final solutions to odd numbered exercises, it does not show the work. As such, I'm stuck in the process of getting from point A to point B:
Find the derivative y'(x) implicitly of...