Calculus Answers

Differentiate y w.r.t x
1. ) y =√(x+√(x+√x))
2.y=e^cosx+cos(e^x )
3.y=ln(x lnx)

Tracing of curve y^2=x(x-2)^2

Let f(x)=sinx,x=0 and Δx be a small change in x. Find a first approximation to sin(Δx). Use this to say whether sin(Δx)≈Δx is true or false.

A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the number of cakes sold per day, and p is price. The total cost function of the company is given by c = (30+5x) 2 where x is previously defined, and c is total cost. A. Find the revenue and marginal revenue functions [Hint: revenue is price multiplied by quantity i.e. revenue = price × quantity] .B. Find the fixed cost and marginal cost function [Hint: fixed cost does not change with quantity produced] . C. Find the profit function [Hint: profit is revenue minus total cost] . D. Find the quantity that maximizes profit.

A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the number of cakes sold per day, and p is price. The total cost function of the company is given by c = (30+5x) 2 where x is previously defined, and c is total cost.
A. Find the revenue and marginal revenue functions [Hint: revenue is price multiplied by quantity i.e. revenue = price × quantity] .B. Find the fixed cost and marginal cost function [Hint: fixed cost does not change with quantity produced] . C. Find the profit function [Hint: profit is revenue minus total cost] . D. Find the quantity that maximizes profit.

Calculate the expected percentage error

Theory says that the pendulum should follow the rule:

T=2π√(L/g)

Where T is the time period (seconds)

L is the length of the pendulum (metre)

G is the acceleration due to gravity (g = 9.81 m/s2)

Calculate the expected percentage error in the time period calculation if your measurement of length is 3% to long?

A certain company manufactures a certain product, P , from three raw materials, combined according to a production function given by
2/5 1/5 1/5 P=50x y z .
Since the budget available for the purchase of the three raw materials of 24000 euros and knowing that they cost for unit 80, 12 and 10 euros, respectively, for x, y and z, what combination should you have regarding the purchase of products x, y and z, in order to maximize production?

A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the number of cakes sold per day, and p is price. The total cost function of the company is given by c = (30+5x) 2 where x is previously defined, and c is total cost.
A. Find the revenue and marginal revenue functions [Hint: revenue is price multiplied by quantity i.e. revenue = price × quantity]
B. Find the fixed cost and marginal cost function [Hint: fixed cost does not change with quantity produced]
C. Find the profit function [Hint: profit is revenue minus total cost]
D. Find the quantity that maximizes profit

Integration of [(a√(a-x))/√(a+x)]

Find an equation of the tangent line to the curve y = ln(x + 3) when x = -2.