Calculus Answers

 A spotlight on the ground is shining on a wall 24m

 away. If a woman 2m

 tall walks from the spotlight toward the building at a speed of 1.2m/s,

 how fast is the length of her shadow on the building decreasing when she is 2m

 from the building?

The equation for a distance, s(m), travelled in time t(s) by an object starting with an initial velocity u(ms^-1) and uniform acceleration a(ms^-2) is:

Given that y=x−m what is dydx?

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

What is Integration? Discuss types of Integration with Example.

the equation of a curve is given as f(x)= sqrt 2x-1, find the equation of the tangent line to the graph of f(x) at x=5

Find the area of the region enclosed by the graphs of y= 3/x and y=4-x

Find the area of the region enclosed by the graphs of f(x)=x³ and g(x)=x²+2x

[Verify your answer by MATHEMATICA and attach the printout of the commands and output]

Verify that the function 𝑦 = 𝑐1𝑒 (−𝑘+2𝑖)𝑥 + 𝑐2𝑒 (−𝑘−2𝑖)𝑥 is a solution to 𝑦 ′′ + 2𝑘𝑦 ′ + (𝑘 2 + 4)𝑦 = 0.

The graph of the parametric equations is called a cycloid.

x=θ-sinθ and y=1-cosθ for 0≤θ≤2π

(a) find dy/dx

(b) find an equation of the tangent to the cycloid at the point where θ=π/3

(c) at what point is the tangent horizontal?

(d) graph the cycloid and the tangent lines in parts (b) and (c)