Chapter 8.5, Problem 1E

A train moves along a track at velocity v. Bionica walks down the aisleof the train with velocity u in the direction of the train' s motion. Computethe velocity w of Bionica relative to the ground using the laws of bothGalileo and Einstein in the following cases: (a) v = 500 m/s and u = IO m/s. Is your calculator accurate enough todetect the difference between the two laws?(b) v = 107 m/s and u = 106 mis.

Differentiate the functions. a) f(x) = 2 – 3x +x b) f(x) %3D Зе* + sinx c) f(x) : 3x d) f(x) = (1 – 3x²)· e*

Can you help me solve this different parts of this problem?

Let fAx) =x' + 4x + 20. a) Explain using Calculus whyf has an inverse function (invertible). b) If g(x) =S '(x), find the equation of the line tangent to the graph of g at x = 4.

Let f(v) be the gas consumption in liters/km of a car traveling at velocity v km/hr. In addition, you know that f(60) = 0.05 and f'(60) = 0.0005. (a) Let g(v) be the distance in km that the car goes on one liter of gas at velocity v. What is the relationship between g(v) and f(v)? O g(v) = f(v) O g(v) = O g(v) = v.f(v) O g(v) = f(v) V O g(v) = 1 f(v) Find g'(60). O h(v) = (b) Let h(v) be the liters of gas the car uses in one hour at velocity v. What is the relationship between h(v) and f(v)? Oh(v) = f(v) O h(v) V f(v) = O h(v) = v.f(v) Oh(v) = f(v) V 1 f(v) V f(v) Find h'(60).

Using differentials, approximate the change in length of the space diagonal of a parallelepiped of length, width, and height given to be 2 units, 3 units, and 5 units, respectively, when the length increased by 0.1 unit and the width decreased by 0.2 unit, while keeping the height constant

The velocity of a particle moving along a straight line is v(t) = sec(t) tan(t) where v is measured in meters per second and t in seconds. Find the acceleration a(t).

Find the approximation for the Green's function of the one-dimensional acoustic wave equation in the case where velocity is given by: c(x) = aebx , where a and b are real numbers and a > 0. Analyze each case, b 0, in detail.

A particle moves along the x-axis. At time t=0 the particle passes through the origin with speed 8ms-1 in the positive x- direction. The acceleration of the particle at  time t seconds, t is greater than or equal to 0, is (4t^3-12t)ms-2 in the positive x-direction. Find: a) the velocity of the particle at time t seconds  b) the displacement of the particle from the origine at time t seconds  c) the values of t at which the particle is instantaneously at rest