Homework Statement
the original function is ##−6 x^3−3x−2 cosx##
##f′(x)=−2x^2−3+2sin(x)##
##−2x^2 ≤ 0## for all x
and ##−3+2 sin(x) ≤ −3+2 = −1##, for all x
⇒ f′(x) ≤ −1 < 0 for all x
The Attempt at a Solution
this problem is part of a larger problem which says
there is a cubic...
Homework Statement
Find all stationary points of the function
G(x, y) = (x^3)*e^(−x^2−y^2)
Homework Equations
fx=0 and fy=0
The Attempt at a Solution
Gx = 3x^2*e^(-x^2-y^2) +x^3(-2x)e^(-x^2-y^2) = e^(-x^2-y^2)(3x^2-2x^4)
Gx = 0 implies 3x^2-2x^4=0
x^2(3-2x^2)=0
hence x =0 ,+or-...
Hey I'm trying to follow the derivation given here: http://lampx.tugraz.at/~hadley/ss1/studentpresentations/Bloch08.pdf
Homework Statement
As it says in the pdf: "Based on Noether's theorem construct the energy-momentum tensor for classical electromagnetism from the above Lagrangian. L=-1/4...
I'm relatively new to calculus and I have a new chapter in my study which is on the Implicit Function, Implicit Differentiation and Higher Derivatives of a function, the problem is I don't understand the meaning of a 2nd or 3rd or whatever the higher derivative of a function is, what I know is...
After doing a couple courses in physics as well as calculus and differential equations, I was starting to wonder about splitting a derivate, such as ## \frac{dy}{dx} ##, into seperate pieces ##dy## and ##dx##. I know we've never done it in calculus or differential equations because it isn't...
Homework Statement
At 9 P.M. an oil tanker traveling west in the ocean at 18 kilometers per hour passes the same spot as a luxury liner that arrived at the same spot at 8 P.M. while traveling north at 23 kilometers per hour. If the "spot" is represented by the origin, find the location of the...
Homework Statement
After a wild ride on a windsurfer, you head to a lifeguard tower to fly a kite. You stand on the tower, which is 3 meters above the ground and release your kite. You let out 10 meters of string and the kite begins moving according to the following equation:
y(t) = (0.9...
Just something that has been bugging me. Can someone bestow why the first derivative is velocity and the second derivative is acceleration. I want to conceptually understand this.
Thank you
Homework Statement
Find f'(x) if f(x) = 8^(sin^2(3x))
Hint: you will need to use the double angle formula for trig functions and your answer should only have one trig function in it.
Homework Equations
if y=a^u then y' = ln a * a^u * du
sin(2x) = 2sinxcosx
The Attempt at a Solution
We're...
Mod note: Thread moved from Precalc section
Homework Statement
F(x)=sqrt(-2x^2 +2x+4)
1.discuss variation of f and draw (c)
2.find the equation of tangent line to (c) that passes through point A(-2,0)
The Attempt at a Solution
I solved first part I found the domain of definition and f'(x)...
Homework Statement
Find the distance between the origin and the line tangent to ##x^\frac{2}{3}+y^{\frac{2}{3}}=a^{\frac{2}{3}}## at the point P(x,y)
Homework Equations
[/B]
Distance= ##\frac{\left |a_{0}+b_{0}+c \right |}{\sqrt{a^{2}+b^{2}}}##
The Attempt at a Solution
To begin I find...
If my understanding is correct the definition of a derivative is lim h->0 (f(x+h)-f(x))/h However, I've also seen this used: lim x->c (f(x)-f(x))/(x-c) are these both considered valid definition for the derivative or does the derivative have to tend towards zero? I am a bit confused because I...
Homework Statement
for ##0<\alpha,\beta<2##, prove that ##\int_0^4f(t)dt=2[\alpha f(\alpha)+\beta f(\beta)]##
Homework Equations
Mean value theorem: ##f'(c)=\frac{f(b)-f(a)}{b-a}##
The Attempt at a Solution
I got the answer for the question but I have made an assumption but I don't know if...
Homework Statement
a. k(t) = (sqrt(t+1))/(2t+1)
b. y = (3^(x^2+1))(ln(2))
The Attempt at a Solution
For the first problem, I know I use the quotient rule for derivatives (L)(DH)-(H)(DL)/((L)^2)
which would go to: ((2t+1)(1/(2sqrt(t+1)) - (sqrt(t+1))(2))/((2t+1)^2) I get stuck here, maybe...
Suppose we have a Kalman filter. We have a position sensor, for example GPS. We use the filter to estimate position. However in all examples I see higher derivatives in the state vector: speed, acceleration and sometimes jerk. There is no sensor that calculates these values directly, so they...
What's the matter:
So, I think I have some skills when it comes to differentiation after taking calculus 2 last semester, but when it starts to intertwine with physics, and interpreting physical phenomenon through equations, It appears I could use some help. Anyway, the problem that I got hung...
Hi all, first post here. I'm a junior Physics/Math double major at UMass Amherst, playing with some problems over the summer. I'll get right into it.
A rope with constant tension T is deflected through the angle 2\theta_{0} by a smooth, fixed pulley. What is the force on the pulley?
It is...
As part of a personal musicology project I found myself with the mathematical model of a geometry which utilizes the equation
a*(a/b)sin(pi*x)
The only problem with this is that I need to take the integral from -1/2 <= x <= 1/2, and according to Wolfram Alpha no such integral exists. I can...
I'm looking for a book to self-study this summer before my last course of Bachillerato (A Levels or High School in other countries).
My performance in Mathematics has only improved and I've just been given the maximum mark this last term (10/10 or A+). This has motivated me a lot to keep...
Let G be a non-empty open connected set in Rn, f be a differentiable function from G into R, and A be a linear transformation from Rn to R. If f '(a)=A for all a in G, find f and prove your answer.
I thought of f as being the same as the linear transformation, i.e. f(x)=A(x). Is this true?
Hey guys and gals, I'm taking an online physics course just to kind of learn the basics before I take the real thing this summer. The course is from OpenYale for those interested (oyc.yale.edu). Anyways, the professor was talking about some formulas for finding ##\vec{r}(t) = r(i(cos\omega t) +...
I have attached an image of a function that I fit to a scatter plot, and I would like to know if there is a term for the point on the function at which the slope transitions from being less than -1 to greater than -1. I have highlighted this point approximately in yellow...
Homework Statement
The website says this:
"It is Linear when the variable (and its derivatives) has no exponent or other function put on it.
So no y2, y3, √y, sin(y), ln(y) etc, just plain y (or whatever the variable is).
More formally a Linear Differential Equation is in the form:
dy/dx +...
Homework Statement
Given two curves y=f(x) passing through (0,1) and ##g(x)=\int\limits_{-\infty}^xf(t)dt## passing through (0,1/n). The tangents drawn to both curves at the points with equal abscissae intersect on the x-axis. Find y=f(x).
Homework Equations
None
The Attempt at a Solution...
I'm hoping someone can clarify for me, I have seen the following used:
\frac{\partial}{\partial g^{ab}}\left( g^{cd} \right) = \frac{1}{2} \left( \delta_a^c \delta_b^d + \delta_b^c \delta_a^d\right)
I understand the two half terms are used to account for the symmetry of the metric tensor...
Homework Statement
[/B]
use richardson extrapolation to estimate the first derivative y=ln(x), x=5 using steps of 2, 1, 0.5. Four decimal points. obtain true relative error for the last estimate and comment on its value.
Homework Equations
[/B]
deriv ln(x)=1/x
The Attempt at a Solution
I...
Hi all,
I have a question concerning the derivative of the formula of the number of nuclei. I hope I've posted this in the right section, I'm new here :P. Anyway, in the question, the given values are:
At a certain time t, there is an amount of radioactive Br-82. The activity A is 7.4*1014 Bq...
Suppose someone gives you a rectangular sheet of length a and width b (so b ≤ a). You make a topless box by cutting out a square with length x out of each corner and folding up the sides. How should you cut the sheet so as to maximize the volume of your box?
Homework Statement
f(x) = 1/ln (10-x) -- I would assume it to be a fairly simple equation, but I am screwing it up
Homework Equations
What is f'(x)?
The Attempt at a Solution
f'(x) = (ln (10-x))^-1
= -(ln (10-x))^-2 * -1 * 1/(10-x) -- 2 negatives cancel out
= 1/(10-x)...
<<Moderator note: Remember that filling in the complete homework template is mandatory in the homework forums. This thread has not been deleted due to containing relevant replies.>>
1. Homework Statement
((x)^(1/x))'
Homework Equations
This probably isn't overly dificult, but it has got me...