A few Multiple function product rule refresher videos later...
I believe the 1st term should go from:
-r \frac{d\theta}{dt} \sin(\theta)
to:
- \left( \frac{dr}{dt} \frac{d\theta}{dt} \sin(\theta) + r \frac{d}{dt}(\frac{d\theta}{dt} \sin (\theta)) \right)
- \left( \frac{dr}{dt}...
Ah yes, it's been 5 years since I typed anything in LaTeX either, but I wrote it correctly on my paper. Now I need a refresher on getting the second derivative of the equation.
I have:
\vec{r} = r \cos(\theta) \hat{i} + r \sin(\theta) \hat{j}
\vec{v} = \left( -r \dot{\theta} \sin(\theta) +...
Ok, so I don't need to chain rule the 1st cosine factor, and adding the chain rule on the cosine factor on the left: \cos(\theta) \cdot \frac{d\theta}{dt}
gives:
\frac{dx}{dt} = \frac d {dt}\left(r\cos(\theta)) \right) = \frac {dr}{dt} \cos(\theta) + r \cdot \left(\cos(\theta) \cdot...
I get that r is the magnitude of \vec{r}
Both r and \theta are functions of time.
Let me start with only the x-side of the equation:
x = r \cos (\theta)
Applying the product rule to r and \cos(\theta) yields:
\dot{x} = r (-\sin)(\theta) + \dot{r} \cos (\theta)
And adding the...
Homework Statement
This is a problem from Dynamics but I'm mostly having trouble with the calculus.
Derive an expression for the position, velocity, and acceleration of a machine in terms of: r, \dot {r}, θ, \dot{θ}, \ddot{r}, \ddot{θ}, .
r = length of the arm
θ = angle of the arm to the...
So, i assume math 111 is College Algebra/ Pre-Calc, and 112 is Trig.
There are usually several General-Education classes that have to be taken as well as ME specific classes, you can always take those while you complete the math sequence. I do not know your specific course requirements (or...
Well, from a quick google search I think Math 65: Developmental elementary algebra, and Math 95: Developmental Intermediate Algebra, but I'm not sure if your school allows you to take Calculus 1 after that.
I do not know if you can finish a ME degree before your GI bill runs out, but it does...
I am 32 and married to my wife for almost 3 years and we are expecting twin boys due in October. I have been attending CC for 2 years part time getting my gen-ed requirements, and the first 2 years toward a mechanical engineering degree, out of the way. And I may be here another 2 years before...
Summer:
Work full time,
Gen Ed......Macroeconomics
Fall:
Continue working full time,
Linear Algebra
Calc-based Physics 1 (online, including lab)
Become Daddy of twin boys!
I understand your frustrations, and yes this does seem like a big sacrifice. I, too, hope it will be worth it in the end. I currently work 45hrs per week and attend community college part time (10hrs of online and night classes).
I finally have most of my gen-ed classes out of the way, but...
In this formula?(f^{-1})(a)=\frac{1}{f'((f^{-1})(a))}
(f^{-1})(a)=\frac{1}{f'(1)}
then
f'(1)=\frac{1}{2}(25)^{-\frac{1}{2}}(6)
equals 3/5, and the inverse is 5/3.
So, is this the way I should go about these kind of problems?
Well, f(5)=\sqrt{177}\approx13.304
So, is the inverse 1/13.304, but then what is the derivative of the inverse?
Or the inverse of the derivative??? at a=5f'(x)=\frac{1}{2}({x^{3}+x^{2}+x+22})^{-\frac{1}{2}}(3x^{2}+2x+1)
f'(5)=\frac{66}{2\sqrt{177}}...
Homework Statement
Find (f^{-1})'(a) of: f(x)=\sqrt{x^{3}+x^{2}+x+22} ; a=5.
Homework Equations
(f^{-1})'(a)=\frac{1}{f'((f^{-1})(a))}
The Attempt at a Solution
Well, I know to find an inverse: I need to set the equation equal to y, solve for x, then swap x and y. But I don't...
I am just starting Calc 2 using the Stewart Calculus book, but I'm finding it harder to understand than the book I used for Calc 1 (Calculus by Briggs and Conchran). I wish I still had that book.
I think I will be buying an additional Calculus book to try and get a different perspective on...
So,
\frac{d}{dx}(ye^{x})=ye^{x}+y'e^{x}
giving me,
xe^{y}y'+e^y+ye^{x}+e^{x}y'=0
y'(xe^{y}+e^{x})=-e^{y}-ye^{x}
y'=\frac{-e^{y}-ye^{x}}{xe^{y}+e^{x}}
at point (0,1).
slope=(-e-1)
Homework Statement
Find an equation of the tangent line to the curve xe^y+ye^x=1 at point (0,1).
Homework Equations
I do not recall seeing the Implicit Function Theroem before, I even went back in my book (Stewart Calculus 6th) to check. I found this post but it does not help me...
You need to check with your CC and any universities where you may plan on transferring, and see if they have a transfer agreement. Most of the "engineering core" classes that can be taken at a CC, seem to be math, physics, and chemistry.
I am currently taking classes at a CC with a transfer...
It is scary how similar this is to the statement I am planning to write. I too, have a English professor father-in-law, a 4.0, am pursuing an engineering degree, and my successful career has left me wanting to learn more. No military experience though, but thank you for your service.
I have...
Your crayon still has me surpassed:
Calculus 2 (4hrs)
Speech (3hrs)
Intro to Sociology (3hrs)
Ten hours while working 45 is all I can handle, even with 2 gen-ed classes.
Thanks, so...
2e^{\frac{ln12}{2}}=2\sqrt{e^{ln12}}=2\sqrt{12}
=4\sqrt{3} and
2\sqrt{e^{ln6}}=2\sqrt{6}
giving me:
\pi((4\sqrt{3}-\frac{1}{12})-(2\sqrt{6}-\frac{1}{6}))
\pi(\frac{1}{12}+4\sqrt{3}-2\sqrt{6})
But that was wrong, and I am unsure how to get the correct answer.
How does that...
Sorry, maybe I have made a mistake in my prior work. (this may need to be moved to the calculus section)
The problem states: Use the washer method to find the volume of the solid when the region bounded by y=e^(x/2) and y=e^(-x), x=ln6, x=ln12, when the region is revolved around the x-axis...