Determining the values to make a function undefined.

For what values or range of values are the following functions undefined a) f(x) = 1/x b) g(x) = Square root of (x+2)(x-3)
c) h(x) = 5 / x^2-4x-45

Find the domain and range of the functions

State the domain and range for each of the following functions (a) f(x) = ln(1 + x squared) (b) f(x) = 1 / (over) x-1 + 1 / (over) x-2

A proof that for a self adjoint linear operator T, (Tf,f) is real for all f in the Hilbert space H, where (f,f) denotes the inner product on H.

Prove that for any self-adjoint bounded linear operator T on a Hilbert space H that (Tf,f) is real-valued for all f in H.

Functions

There are two functions: f(x)=(x^2+x-12)/(x^2+6x+18) and g(x)=(x-3)/(x+2) If you take the first derivation of both functions, they should be equal. Please explain why.

Integrals: Cost function and Marginal Cost

Given ist the following cost function: k(x)=x^3-9x^2+29x+35 x= quantity k= cost question 1: At what quantity is the minimum of the marginal cost? question 2: What is the increase of cost if the production is increased from 3 to 4 (integral)?

Accounting: Objective function and equation

A company has the opportunity to produce 3 products (P1; P2; P3) out of 3 Materials (A1; A2; A3). The estimated margin of the products is: P1= 10$, P2= 6$ and P3= 4$ Please evaluate in which quantity the products have to be produced to show the highest margin possible: Material P1 P2 P3 Available Quantity A1 2 1 6 ...continues

Optimization problem dealing with a fence and area.

A farmer has 600 feet of fencing with which to enclose a rectangular plot. What is the maximum area he can enclose? Hint: Find a model for the area of the rectangular plot and maximize by completing the square

Formula for a sine curve given the amplitude and either the period, frequency or angular frequency.

(i) In london in 2002, the maximum number of daylight hours in a day was 16.63, and this was recorded in week 25.The minimum number of daylight hours in a day was 7.82, and this was recorded in week 51. The number of daylight hours in a day can be modelled approximately by using a sine function. Use the information given abo ...continues

Calculus : Partitions and Riemann Integral

Let f be the function: F(x) 1/4 x=o, x 0 ...continues

Using Regression Functions

Demonstrate using regression functions by explaining what a regression function is and the factors which should be considered when interpreting results.