DERIVE EXPRESSION

An object is thrown downward from the top of a building with an initial velocity of 30 m/s. Assuming a positive direction of y measured downward from the top, derive an expression for (a) the velocity and (b) the displacement as a function of time. Assume y(0)=0

Theoretical statistics proof using calculus

see attachment

Homogeneous differential equation

Solve the homogeneous differential equation. dy/dx = (x^3+y^3)/(xy^2)

Vector Functions to Partial Derrivative

Attached is more clear 1. Distance from a a point to a curve: Find the shortest distances between the point (1,2,1) and a point on the curve r(t)= (1/t*i)+(lnt(t)*j)+(sqrt(t)*k) 2. Distance from a point to a curve: Find the maxmium distances from the point (1,2,-1) to a point on the curve of intersection of the plane z=( ...continues

Taylor Series

Use long division to find a Taylor series expansion of f(x) = cosx/( 1 + sinx) about x (sub 0) = 0 from those of cos x and sin x. How do we know this is the correct Taylor series for cos x/( 1 + sinx)

Convergence with integration

Use these two facts 1) integral from 0 to pi/2 of log x dx converges 2) sinx >= (2x/pi)^2 on [0, pi/2] to show that integral from 0 to pi/2 of ln(sinx)dx converges

Limits

I attached a word document. Be sure to show me all of your work so that I can fully understand how to do the problems correctly. Thank you very much for your help.

Calculus Help

I attached the problems that I would like you to do. I have already completed these problems by myself, but would like to see if I did them correctly and would like to compare your answers with mine so that I know which problems I mastered and which I need to study up on. Thank you.

Largest interval

View attachment

Linear or nonlinear

view attachment