Calculus Answers

A firm's average revenue function 

𝐴𝑅=−18−7,5𝑄+𝑄

2

.

AR=−18−7,5Q+Q2.

Determine the number of units to be produced and sold to maximise revenue.

a.−1

b.6

c.3,75

d.0

The demand function of a firm is 

𝑄=90−1,5𝑃,

Q=90−1,5P,

where 𝑃

P and 𝑄

Q represent the price and quantity, respectively. At what price is revenue a maximum?

a.15

b.30

c.270

d.90

ACTIVITY IN BASIC CALCULUS

BASIC RULES IN DERIVATIVE

 Complete the blanks of the given function below with a number (except 0 and 1) to create your own problem and find the derivative of the function. Show your complete solution to each problem.

1. f(x) = -4x5 + ______x-4- 2468

2. f (x) =____x-3- _____x1/4 - 12x

3.f(x)= ____ "\\sqrt[4]{x}" ³ - "\\underset{x^6}{=}" + "\\frac{2}{3}" x⁶

4.f (x) = "\\underset{x^-6}{=}" - ____x² + "\\sqrt[4]{x}"

Differentiate the following functions:

1.y=1/2(3x^2+1)^2

2.y=3+4x-x^2

Find the derivative of the following

1.y=√x^2-2/2x^3+1

2.y=x^2√6x^2/3x

3.y=2x^2√x

Evaluate the following integrals

(1) integral of {(10x^9+40x^4+3)√(x^10+8x^5+3x+5)} DX

(2) integral of {1/[(x-5)(x^2+4)]} dx

ACTIVITY IN BASIC CALCULUS

BASIC RULES IN DERIVATIVE

Name: ____________________ Grade & Section: _______________ Date: __________

  Complete the blanks of the given function below with a number (except 0 and 1) to create your own problem and find the derivative of the function. Show your complete solution to each problem.

 1. f (x) = -₄x⁵ +___x^-4 - 2468

2. f (x) =____x^-3 - ____x^1/4 - 12x

3.f (x) =____"\\sqrt[4]{x}" ³ - "\\xlongequal{x}"

 4. ( )

√

The temperature at a point is given by T = xyz. Find the average temperature in the cube

with opposite corners at (0,0,0) and (2,2,2).

Determine the average value of F(x, y, z) = xyz throughout the cubical region D

bounded by the coordinate planes and the planes x = 2, y − 2, z = 2 in the first octant.

ACTIVITY IN BASIC CALCULUS

BASIC RULES IN DERIVATIVE

  Complete the blanks of the given function below with a number (except 0 and 1) to create your own problem and find the derivative of the function. Show your complete solution to each problem.

1. f(x) = -₄x⁵ + ______x^-4- 2468

2. f (x) =____x^-3- _____x^1/4 - 12x

3.f(x)= ____ "\\sqrt[4]{x}" ³ - "\\xlongequal{}"

4.f (x) = "\\xlongequal{}" - _____x² + "\\sqrt[4]{x}"

Find the volume of the region bounded above by the plane z = y/2 and below by the

rectangle.

R ∶ 0 ≤ x ≤ 4,0 ≤ y ≤ 2