Search
Describe any three inference rules
Reflect on the concept of polynomial and rational functions. What concepts (only the names) did you need to accommodate these concepts in your mind? What are the simplest polynomial and rational function you can imagine? In your day to day, is there any occurring fact that can be interpreted as polynomial and rational functions? What strategy are you using to get the graph of polynomial and rational functions?
1. a) Define differentiation and integration in calculus. Also write down the differences between them.
b) Write down some application of Calculus in CSE.
c) Describe geometrical meaning of definite integral with figure.
There are 21 pupils in a grade 7 class. The class teacher has to choose eight of the pupils for a group that will visit Germany in three months time. In how many different ways can the teacher select pupils for the group ?
1. You wanted to start your business of manufacturing custom made mobile covers for the newest model of iPhone. The selling price is per cover. The cost function to manufacture the covers is where is the number of covers sold. Show at least 5 decimal places
a. Find the profit function . 3 Marks
b. Find the quantity that maximizes profit. 2 Marks
c. Explain the steps you take to arrive at your answer in part b. 3 Marks
d. Interpret the answer. 2 Marks
Differentiate the following functions.(use Chain Rules)
1. y=(5x² —2x + 1)—³
The manufacturer of television tube know from the past experience that the average life of tube is 2000 hrs with a s.d. of 200 hrs a simple of 100 tubes has an average life of 1950 hrs test at the 0.01 level of significance to see if this sample come from a normal population of mean 2000 hrs.
1a) Use set-builder notation to prove that
A-(B ∩C)=(A-B)∪(A-C)
b) Let E={ 1,23,4,5,6,7,8,9,10} and ordering of element in increasing order that is a= i; what bit strings represent the subsets of integers not exceeding 5 in E
3a)Let A={1,2,3},determine all partitions of A
A small factory producing a single product has weekly fixed costs of production of $2,112 and weekly variable costs of $52x + 3/4 x2, where x is the quantity produced. the capacity of the factory is about 600 units.
Past experience suggests that the product’s price and quantity are linked by the following demand equation: p = 200 - 1/4 x (p, x > 0) where p = $ price/unit and x = quantity sold. You are required to:
(a) Find the level of production at which revenue is maximized
(b) Find any break-even points
6. A company manufacturing wicker baskets knows that it has variable costs of $0.62 per unit and fixed costs of $150 per week. Its baskets sell for $2.40 each. Assuming that total costs are a linear function of output, calculate the level of weekly sales necessary to:
(i) Break-even
(ii) Reach a profit of $4300 per week
