Using Related Rates In Exercises 1–4, assume that x and y are both differentiable functions of t. Use the given values to find (a) dy/dt and (b) dx/dt. See Example 1.
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Calculus: An Applied Approach (MindTap Course List)
- a) compare E(Y|X=x) and E(Y|X) b) Find the pdf of Y c) find the conditional pdf of X given that Y=yarrow_forwardDeteremine the area between the curves y= sin(x), y= x^2 + 4, x= -1, and x=2.arrow_forwardUsing Properties of the Derivative In Exercise 26, use the properties of the derivative to find the following. (a) r′(t) (b) d dt [u(t) − 2r(t)] (c) d dt [(3t)r(t)] (d) d dt [r(t) ∙ u(t)] (e) d dt [r(t) × u(t)] (f) d dt [u(2t)] 26. r(t) = sin ti + cos tj + tk, u(t) = sin ti + cos tj + 1 t k * only d ,e, f *arrow_forward
- fxy(x,y)=c(x+y) find c for fxy to be a joint PDF. 0<x<3 and 0<y<xarrow_forwardDetermine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If y is a differentiable function of u, u is a differentiable function of v, and v is a differentiable function of x, then dy/dx = dy/du du/dv dv/dx.arrow_forwardUsing a Differential as an Approximation, f(x, y) = 16 − x2 − y2 find f (2, 1) and f (2.1, 1.05) and calculate ∆z, and use the total differential dz to approximate ∆z.arrow_forward
- Explain why the function is differentiable at the given point. Then find the linearization L(x,y) of the function at that point. f(x,y)=y+sin(x/y),(0,3)arrow_forwardStokesTheorem.Evaluate∫ F·dr,whereF=arctanx/yi+ln√x2+y2j+k and C is the boundary of the triangle with vertices (0, 0, 0), (1, 1, 1), and (0, 0, 2).arrow_forwardUsing a Differential as an Approximation f(x, y) = x cos y, find f (2, 1) and f (2.1, 1.05) and calculate ∆z, and use the total differential dz to approximate ∆z.arrow_forward
- Find the linearization L(x) of the function at a. f(x) = sin(x), a = ? 6arrow_forwardUsing Properties of the Derivative In Exercise 26, use the properties of the derivative to find the following. (a) r′(t) (b) d dt [u(t) − 2r(t)] (c) d dt [(3t)r(t)] (d) d dt [r(t) ∙ u(t)] (e) d dt [r(t) × u(t)] (f) d dt [u(2t)] 26. r(t) = sin ti + cos tj + tk, u(t) = sin ti + cos tj + 1 t karrow_forwardaverage velocity over time interval (to, t1) v(avg)=s(t1)-s(t0)/t1-t0=1/t1-t0∫t1 v(t)dt t0 Find a template for the average acceleration of a particle (in rectilinear motion) over time interval (t0, t1) suppose that the acceleration function of a particle moving along a coordinate line is a(t)=t+1. Find the average acceleration of the particle over the time interval (0,5) by integrating. suppose that the velocity function of a particle moving along a coordinate line is v(t)=cost. Find the average acceleration of the particle over the time integral (0,pi/4) by integragting.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning