Calculus Answers

Evaluate:

1. &Integral ³ (x² -4x + 4x ^{– 2}) dx

The demand function of a commodity at a sales price p is given by: D(p) = 700/p − 250 p^2−0.002p Find the elasticity of demand and the price of unit elasticity(meaning what is p when |E(p)| = 1).

If del f =2xyz³ i + x²z³ j+ 3x²y²z² k find the f(x,y,z) at f(1,-2,2)

1. Determine the general form of the equation of the circle whose center is (3,2) and

whose graph contains the point (1,2). Sketch the graph.

2.Write the general equation of the circle whose center is (5, -1) and whose radius is 4.

Sketch the graph.

3.Convert the equation x^2 + y^2 + 2x − 6y + 7 = 0 to standard form and sketch the graph.

4.4. Change the equation (x − 2)^2 + (y − 6)^2 = 9 to general form and sketch the graph.

2. SEQUENCE. 

A. Consider the sequence {Sn} defined by Sn = 2n – 5 where −4 < 𝑛 ≤ 4.

Show complete solution. 

Find for: 

a. 1st element 

b. 5th element 

c. A7 

d. A10 

e. ∏𝑨𝒊

i=3

f. 5

∑𝑨𝒊

i=1

Thinking Box:

The sequence {An} defined by An = 2n – 5 where 𝒏 ≥ 𝟏 is an example of finite or infinite sequence? Why?

Prove that the union of two closed sets is a closed set. Give an example to show that union of an infinite number of closed sets need not be a closed set.

 [x^v Y_{v (x)}]= x^v Y_v-1(x)

Determine the value of the arbitrary constant of the antriderivative of given the initial value

x = 7.03 and y = 8.75 . (Use 2 decimal places)

How can we produce the terms of a sequence if the first 10 terms are 1, 2, 2, 3, 3, 3, 4, 4, 4, 4?

Find the area of the surface generated by revolving the curve

y

=

5

√

x

,

y=5x,

       2

≤

x

≤

4

2≤x≤4

around the x

x

-axis.