around so-called schlicht functions—that is, functions regular in a given domain and assuming no value there more than once. The type of problem we consider involves determination of precise bounds for certain quantities depending on the function/, as ƒ ranges over the schlicht functions in question. Since, for suitable normalization of the functions at some fixed point of the domain, the resulting family of functions is compact or normal, the extremal schlicht functions always exist and the problem
Words: 3481 - Pages: 14
CHAPTER 7 CHAPTER 8 CHAPTER 9 : : : : : : : : : Functions Quadratic Equation Quadratic Function Simulataneous Equation Indices and Logartihms Coordinate Geometry Statistics Circular Measures Differentiation Solution of Triangles Index Number CHAPTER 10 : CHAPTER 11 : MATHS 2 3472/1 2012 Maths Catch Network © www.maths-catch.com [Lihat halaman sebelah] SULIT MATHS Catch SPM 2012 USAHA +DOA+TAWAKAL FOKUS A+ GEMPUR CHAPTER 1: Function Exam Year: ADDITIONAL MATHEMATICS FORM 4 / TINGKATAN
Words: 7475 - Pages: 30
Consider the function f(x)=(e^2x-1)/x Find the limit of f(x) as x approaches zero. 2. Define the function Find the derivative of that function. Find f’(0.67) (the first derivative at 0.67). What does that mean for the function f at the point? Find f’’(0.67) (the second derivative at 0.67). What does it mean for the function f at that point? Find all points where the derivative is zero. A) B) C) D) 3. Define the function Find the derivative of the function and use
Words: 290 - Pages: 2
|[pic] |Syllabus | | |College of Natural Sciences | | |MTH/208 Version 5 | |
Words: 2247 - Pages: 9
ASSIGNMENT 2 QUESTION 1 a) Suppose the monthly revenue and cost functions (in dollars) for commodity produced and sold are: ( ) = 400 − and units of a ( ) = 5000 + 70 respectively. i) Find the profit function. Solution: [2 marks] Revenue function R(x) = 400 − 20 Cost function C(x) = 5000 + 70 Profit Function is defined as ( )= ( )− ( ) = 400 − ( ) = 330 − ii) − 5000 Find the marginal profit function. [2 marks] Solution: Marginal profit is the difference
Words: 846 - Pages: 4
pairs for the function ( ) = 2 , as well as its graph. Inputs Outputs −2 −1 0 1 2 ( ) (−2) = 4 (−1) = 1 (0) = 0 (1) = 1 (2) = 4 Ordered Pairs (, ( )) (−2, 4) (−1, 1) (0, 0) (1, 1) (2, 4) I have plotted the ordered pairs above in the graph below. Function f 1 Example 1: Use the function on the previous page, its table, and its graph to answer the following: a. How can the function ( ) = 2 + 2 be written in terms of the function ? ( ) = (
Words: 2324 - Pages: 10
that A and B are available for production are 40 and 34, respectively. The profit per unit on X, Y, and Z is $10, $15, and $22, respectively. 4. (a) Find the limit of [pic] and [pic]. (b) Find the first order derivative of the following functions. (i) y = ex+y, where y = y(x) and (ii) f(x) = [pic]. 5. Find an equation of the tangent line
Words: 369 - Pages: 2
Math 5616H Midterm 1 with solutions Spring 2013 March 8, 2013 Total 80 points 1. (15 points) Let f (x) and g(x) be real continuous functions on an interval [a, b], such that b b f 2 (x) dx = a a b g 2 (x) dx = 1. Prove that a f (x)g(x) dx ≥ −1, and that a b f (x)g(x) dx = −1 if and only if f ≡ −g on [a, b]. Answer: Since f and g are continuous, so is (f + g)2 , which is therefore integrable. We compute: b b b b b 0≤ a b [f (x)+g(x)]2 dx = a f (x)2 dx+2 a
Words: 966 - Pages: 4
coordinates of all relative extreme points of[pic]. |A)[pic] |B) [pic] |C) [pic] |D) [pic] |E) [pic] | [pic] First find the derivative of the function[pic], f ’(x): |[pic] |= |[pic] |apply power rule of differentiation | | |= |[pic] |simplify
Words: 1643 - Pages: 7
Polynomial functions mc-TY-polynomial-2009-1 Many common functions are polynomial functions. In this unit we describe polynomial functions and look at some of their properties. In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature. After reading this text, and/or viewing the video tutorial on this topic, you should be able to: • recognise when a rule describes a polynomial function, and write down the degree
Words: 2680 - Pages: 11
