# derivative

1. ### I'm curious what anyone gets for part d

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...
2. ### Why is the first derivative velocity?

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
3. ### Calc BC derivative problem with trig and double angle -- Help please

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...
4. ### How to find the equation of this tangent?

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...
5. ### Finding the distance from origin to a tangent line

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...
6. ### What version of the definition of derivative

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...
7. ### Question on Mean Value Theorem & Intermediate Value Theorem

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...
8. ### Confused on these two derivative problems

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...
9. ### How does the Kalman filter calculate derivatives?

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...
10. ### Velocity Derivative of a Sinusoidal Wave (Counter-Intuitive)

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...
11. ### Tension on a Rope Deflected by a Pulley: Differentials

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...
12. ### 'Wheel-like' Mathematics (Modulating Trig Functions?)

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...
13. ### Foundations What's a good book for last year of A levels Maths?

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...
14. ### Derivatives and Linear transformations

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?

29. ### Proving the fundamental theorem of calculus using limits

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...
30. ### For f(x) = abs(x^3 - 9x), does f'(0) exist

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...