1. 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
1. 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.
2. Homework Equations
if y=a^u then y' = ln a * a^u * du
sin(2x) = 2sinxcosx
3. The Attempt at a Solution...
Mod note: Thread moved from Precalc section
1. 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)
3. The Attempt at a Solution
I solved first part I found the domain of definition and...
1. 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)
2. Homework Equations
Distance= ##\frac{\left |a_{0}+b_{0}+c \right |}{\sqrt{a^{2}+b^{2}}}##
3. The Attempt at a Solution
To begin I...
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...
1. Homework Statement
for ##0<\alpha,\beta<2##, prove that ##\int_0^4f(t)dt=2[\alpha f(\alpha)+\beta f(\beta)]##
2. Homework Equations
Mean value theorem: ##f'(c)=\frac{f(b)-f(a)}{b-a}##
3. The Attempt at a Solution
I got the answer for the question but I have made an assumption but I don't...
1. Homework Statement
a. k(t) = (sqrt(t+1))/(2t+1)
b. y = (3^(x^2+1))(ln(2))
3. 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...
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...
1. 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 +...
1. 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).
2. Homework Equations
None
3. The Attempt at a...
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...
1. Homework Statement
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.
2. Homework Equations
deriv ln(x)=1/x
3. 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?
1. Homework Statement
f(x) = 1/ln (10-x) -- I would assume it to be a fairly simple equation, but I am screwing it up
2. Homework Equations
What is f'(x)?
3. The Attempt at a Solution
f'(x) = (ln (10-x))^-1
= -(ln (10-x))^-2 * -1 * 1/(10-x) -- 2 negatives cancel out
=...
<<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))'
2. Homework Equations
This probably isn't overly dificult, but it has got me...
1. Homework Statement
Hello all, thank you for the help in advance. It's a two-sided derivative problem, for lack of a better term, and I appreciate all hints or help. If we have a function y so that
y=bx for all x<0, and
y= x^2-13x for all x> or = 0,
for what value of b is y differentiable...
Is the time derivative of a curl commutative? I think I may have answered this question.... Only the partial time derivative of a curl is commutative? The total time derivative is not, since for example in cartesian coordinates, x,y,and z can themselves be functions of time. In spherical and...
1. Homework Statement
So the first part asks to prove the time derivative of kinetic energy is dT/dt=F dot product v which I did not problem. but then the second part of the problem asks to prove that if the mass is changing with time then the time derivative of d(mT)/dt=F dot product m and...
When can I do the following where ##h_{i}## is a function of ##(x_{1},...,x_{n})##?
\frac{\partial}{\partial x_{k}}\frac{\partial f(h_{1},...,h_{n})}{\partial h_{m}}\overset{?}{=}\frac{\partial}{\partial h_{m}}\frac{\partial f(h_{1},...,h_{n})}{\partial x_{m}}\overset{\underbrace{chain\...
Would it be a legitimate (valid) proof to use an \epsilon-\delta limit approach to prove the fundamental theorem of calculus?
i.e. as the FTC states that if f is a continuous function on [a,b], then we can define a function F: [a,b]\rightarrow\mathbb{R} such that F(x)=\int_{a}^{x}f(t)dt
Then F...
1. Homework Statement
For f(x) = abs(x^3 - 9x), does f'(0) exist?
3. The Attempt at a Solution
The way I tried to solve this question was to find the right hand and left hand derivative at x = 0.
Right hand derivative
= (lim h--> 0+) f(h) - f(0) / h
= (lim h--> 0+) abs(h^3 - 9h) / h...