Calculus Answers

State is the following statement is true or false. Give reasons for your answers in the form of a short proof or a counterexample.

The domain of the function f defined by f(x)= √(3-x)/(x-2) is R-{2}.

) The function g is related to one of the parent functions g(x) = −(x − 2)^3 a.) Identify the parent function f. b.) Use function notation to write g in terms of f.

You are working as a Junior Engineer for a small motor racing team. You have been given a proposed mathematical model to calculate the velocity of a car accelerating from rest in a straight line. The equation is: 𝑣(𝑡) = 𝐴 (1 − 𝑒 − 𝑡 𝑡𝑚𝑎𝑥𝑠𝑝𝑒𝑒𝑑)

Ascari A10 5.0 V8 - [2006] t=2.8 tm(400)= 10.36 tmaxspeed= 7.8

derive an equation a(t) for the instantaneous position of the car as a function of time? Identify the acceleration of the car at t = 0s and asymptote of this function as t → ∞?

The region in the first quadrant, which is bounded by the curve

x² = 4y, the line x = 4, is revolved about the line x = 4. Locate the

centroid of the resulting solid of revolution.

The region in the first quadrant which is bounded by the curve y² =

4x, and the lines x = 4 and y = 0, is revolved about the x-axis.

Locate the centroid of the resulting solid of revolution.

Given the area in the first quadrant bounded by y^2 = x, the line x =

4 and the x-axis. What is the volume generated when this area is

revolved about the y-axis?

The loop of the curve has an equation of y² = x (1 - x)^2. Find the

area enclosed by the loop of the curve.

The curve has an equation y = e^x. Compute the area bounded by the

curve from x = 0 to x = 1.

The curve has an equation y = e*. Compute the area bounded by the

curve from x = 0 to x = 1.

A curve has an equation of y=sin x. If the area of the curve

y=sin x from x=0 to X=pi is revolved about the y-axis, what is the

volume generated?