Math Answers

Evaluate the following limits,if they exist,where [x] is the greatest interger function

a)lim [2x]/x as x approaches 0

b)lim x[1/x] as x approaches 0

If u=x(1-y) and v=xy, then find the value of the Jacobian ∂u,v∂(x,y)

Select one:

A -x

B x2

C -x2

D x

In a large region, there are 450 farmers. 250 pounds of farm beetroot, 110 pounds of farm yams, 75 pounds of farm radish, 45 pounds of farm beetroot and radish, 40 pounds of farm yams and radish, and 30 pounds of farm beetroot and yams Let B, Y, and R represent the farms that grow beets, yams, and radish, respectively.

Determine the number of farmers that farm beetroot, yams, and radish.

if A=2i+j+k, B=i-2j+2k and C=3i-4j+2k , find the projection A+C in the direction of B.

Round the answer to this question to the nearest rand. David borrowed R911012,00

R911012,00 to refurbish his holiday home. The loan requires monthly repayments over 12 years. When he borrowed the money, the interest rate was 12,4% per annum, compounded monthly, but five years later the bank increased the annual interest rate to 13,9%, in line with market rates. After five years the present value of the loan is R682081,77

R682081,77. With the new interest rate, his monthly payments will increase by

Find out median for the following data

x: 10,15,18,23,27,30,31 f

20,30,40,50,60,70

If the demand function is P = 70 - Q find an expression for TR in terms of Q.

(1) Differentiate TR with respect to Q to find a general expression for MR in terms of Q. Hence write

down the exact value of MR at Q = 60.

(2) Calculate the value of TR when

(a) Q=60 

(b) Q=61

and hence confirm that the 1 unit increase approach gives a reasonable approximation to the exact value of MR obtained in part (1).

2x1^2+4x1x2+5x2^2

Consider the population consisting of values

3, 5, and 7.

a. List all the possible samples of size 2 that can be drawn from the population with replacement in the table below.

b. Find the mean of the sampling distribution of means.

c. Find the variance of the sampling distribution of the means

d. Find the standard deviation of the means

Consider the population consisting of values

3, 5, and 7.

List all the possible samples of size 2 that

can be drawn from the population with

replacement in the table below.

b. Find the mean of the sampling distribution

of means.

c. Find the variance of the sampling

distribution of the means

d. Find the standard deviation of the means