and the number of redundant equations of this system. Further, determine the solution(s) if solutions exists. [10 marks] Question 2. Give formal definitions for the following: (a) a convex function, (b) a strictly con vex set, (c) a differentiable function. Further, give an example of a concave function that is not differentiable. [10 marks] Question 3. Find the solution of the following differential equation = 1 + 3 − 2 ˙ where (0) = 5. [10 marks] Question 4. Find the general
Words: 347 - Pages: 2
Cobb–Douglas Production Functions 1 mathematical tricks • the derivative of αxβ with respect to x is αβxβ−1 • xα xβ = xα+β (for any α and β) • 1 xα = x−α • if m = nB , then n = m1/B 2 the production function A production function y = f (x1 , x2 ) is a Cobb–Douglas production function if it can be written in the form y = Axa xb 1 2 (1) where A, a and b are positive constants. So the partial derivatives of a Cobb–Douglas production function are : M P1 = M P2 = ∂y = aAxa−1
Words: 1446 - Pages: 6
blogspot.com ADDITIONAL MATHEMATICS MODULE 1 FUNCTIONS Organized by Jabatan Pelajaran Pulau Pinang 2006 http://mathsmozac.blogspot.com http://sahatmozac.blogspot.com CHAPTER 1 : FUNCTIONS Contents 1.1 Concept map Page 2 1.2 Determine domain , codomain , object, image and range of relation 3 1.3 Classifying the types of relations 3 2.1 Recognize functions as a special relation. 2.2 Expressing functions using function notation. 2.3 Determine domain , object , image
Words: 2371 - Pages: 10
a) If a and b are constants, evaluate h→0 trig expression involving b&h A correct answer without detailed reasoning will be given little merit. b) Something involving related rates. Q. Obtain the derivative of the following functions, and simplify as far as possible: … functions not shown…say two different part questions involving log,
Words: 424 - Pages: 2
f (a)). The equation of the 1 2 tangent line is y = − 5 x − 25 . Find a, f (a), and the slope of the parabola f (x) at (a, f (a)). 6 (b) Consider the graph of y = x3 . Find the point(s) on the graph where the slope is equal to 11 . (c) The demand function for a commodity with price P is given by the formula D(P ) = a − bP . Find dD(P )/dP . (d) The cost of producing x units of a commodity is given by the formula C(x) = p + qx2 . Find C (x), the marginal cost. Problem 2. (a) Determine the limit limx→0
Words: 420 - Pages: 2
Real-valued functions[edit] A real-valued function f is one whose codomain is the set of real numbers or a subset thereof. If, in addition, the domain is also a subset of the reals, f is a real valued function of a real variable. The study of such functions is called real analysis. Affine functions | Quadratic function | Continuous function | Trigonometric function | An affine function | A quadratic function. | The signum function is not continuous, since it "jumps" at 0. | The sine and cosine
Words: 276 - Pages: 2
maeSome Implications of Belief in the Afterlife and the Allocation of Time to Spirituality∗ Constantino Hevia† University of Chicago September 2004 Abstract An otherwise standard model of intertemporal consumer choice is extended to incorporate the allocation of time to spiritual activities along the lines of the human capital literature. Several testable implications are analyzed. We study exogenous and endogenous changes in life expectancy, and we argue that the traditional value of life or
Words: 7590 - Pages: 31
domain of this relation? (b.) What is the range? (c.) Is this a function? Why or why not? (d.) Is this relation one-to-one? Why or why not? (d.) Define g as {(Mindy, Subaru), (Jasmine, Toyota), (Sharon, VW), (Roger, Kia), (Jose, Oldsmobile)}. Is g a one-to-one function? Why or why not? 2. Prove that the function f : R → R given by f (x) = 4x − 3 is surjective. [You may use the Proof Shuffler applet to help you]. 3. Prove that the function f : [0, ∞) → [4, ∞) given by f (x) = x2 + 4 is bijective. [You
Words: 772 - Pages: 4
Exponential Functions 1. What is the definition of an exponential function? Page 412 An exponential function f with base b is defined by f(x) = bx or y = bx, where b is a positive constant other than 1 (b > 0 and b is not equal to 1) and x is any real number. Example: g(x) = 10^x 2. What is the inverse of an exponential function? Page No horizontal line can be drawn that intersects the graph of an exponential function at more
Words: 315 - Pages: 2
Composition and Inverse Functions provide an opportunity for manipulating expressions using different values. These values can help business owners, data analysts, and even the consumer compare rates and data. Functions also extend independent (x) and dependent (y) variables by graphing in the coordinate plane and creating a visual demonstration of the relationship. The following functions will be used in the required problems. f(x) = 2x+5 g(x) = x2+3 h(x) = (7-x)/3 The first task is to compute
Words: 759 - Pages: 4
