14 The Cumulative Distribution Function 15 Continuous Random
... Remark The above definition also holds for discrete random variables. However, for a discrete random variable the median (and the quartiles and percentiles) may not exist. If the random variable is continuous they are guaranteed to exist. (Which result from calculus implies this?) Definition The prob ...
... Remark The above definition also holds for discrete random variables. However, for a discrete random variable the median (and the quartiles and percentiles) may not exist. If the random variable is continuous they are guaranteed to exist. (Which result from calculus implies this?) Definition The prob ...
SCHOOL OF MATHEMATICS MATHEMATICS FOR PART I
... Rules 1 and 2 on p.636 are very important, but you should note that rule 3 is not usually remembered in that form and rule 4 is not normally used at all, although it is a neat result. Work through parts (a), (b) and (d) of Example 8.42. If you need further practice study Example 8.43. 4. Example 8.4 ...
... Rules 1 and 2 on p.636 are very important, but you should note that rule 3 is not usually remembered in that form and rule 4 is not normally used at all, although it is a neat result. Work through parts (a), (b) and (d) of Example 8.42. If you need further practice study Example 8.43. 4. Example 8.4 ...
Mathematics for Economics: Exercise 2
... (i) Derive the AVC ( average variable cost) function and show that , when AVC is a minimum , MC = AVC where MC is marginal cost. (ii) Derive the ATC (average total cost) function and check that , where q = 5, ATC is a minimum and MC = ATC. (iii) Show that the total cost function has a non-stationary ...
... (i) Derive the AVC ( average variable cost) function and show that , when AVC is a minimum , MC = AVC where MC is marginal cost. (ii) Derive the ATC (average total cost) function and check that , where q = 5, ATC is a minimum and MC = ATC. (iii) Show that the total cost function has a non-stationary ...
Study guide for the third exam
... 4.7), sections 5.1-3.3, and Math Insight parts 18-25. Using the book sections as a guide, the following highlights what is and what is not good potential material for the third exam. 1. Taylor polynomials (section 3.7) Be able to compute linear and quadratic approximations of a function around a poi ...
... 4.7), sections 5.1-3.3, and Math Insight parts 18-25. Using the book sections as a guide, the following highlights what is and what is not good potential material for the third exam. 1. Taylor polynomials (section 3.7) Be able to compute linear and quadratic approximations of a function around a poi ...
Chapter 1
... Continuity at a Point: A function is continuous at c if the following three conditions are met. 1. f (c) is defined. ...
... Continuity at a Point: A function is continuous at c if the following three conditions are met. 1. f (c) is defined. ...
Exam 3 Solutions
... x + 2y = 12 If we solve for λ in both equations 1 and 2 from above, and set them equal, we get 3x2 + 2y = x + 4y. Using the third equation, we have 2y = 12 − x. Plugging this into the previous equation gives 3x2 + 12 − x = x + 2(12 − x) Solving for x gives x = ±2, which gives y = 5 and y = 7 respect ...
... x + 2y = 12 If we solve for λ in both equations 1 and 2 from above, and set them equal, we get 3x2 + 2y = x + 4y. Using the third equation, we have 2y = 12 − x. Plugging this into the previous equation gives 3x2 + 12 − x = x + 2(12 − x) Solving for x gives x = ±2, which gives y = 5 and y = 7 respect ...
Math 147: Review Sheet for Third Test 2.7 Implicit
... (3/4)(4−5/2 )b = 0, or −4a + 3b = 0. Solving these two equations simultaneously yields a = 39/8 and b = 13/2. ...
... (3/4)(4−5/2 )b = 0, or −4a + 3b = 0. Solving these two equations simultaneously yields a = 39/8 and b = 13/2. ...
Block 5 Stochastic & Dynamic Systems Lesson 14 – Integral Calculus
... The Fundamental Theorem of Calculus Let f be a continuous real-valued function defined on a closed interval [a, b]. Let F be a function such that for all x in [a, b] then ...
... The Fundamental Theorem of Calculus Let f be a continuous real-valued function defined on a closed interval [a, b]. Let F be a function such that for all x in [a, b] then ...
aCalc02_3 CPS
... A. f(5) must be positive B. f(2) must be negative C. f(x)=0 must have a solution between 3 and 4 D. f(x) must be a linear equation with a slope of 6 E. None of the above ...
... A. f(5) must be positive B. f(2) must be negative C. f(x)=0 must have a solution between 3 and 4 D. f(x) must be a linear equation with a slope of 6 E. None of the above ...
Density functions Math 217 Probability and Statistics
... of the target has to be between 0 and 1, so we know X ∈ [0, 1]. By definition F (x) = P (X ≤ x), that is, the dart lands within x units of the center. The region of the unit circle for which X ≤ x is a circle of radius x. It has area πx2 . Since we’re assuming uniform continuous probability on the u ...
... of the target has to be between 0 and 1, so we know X ∈ [0, 1]. By definition F (x) = P (X ≤ x), that is, the dart lands within x units of the center. The region of the unit circle for which X ≤ x is a circle of radius x. It has area πx2 . Since we’re assuming uniform continuous probability on the u ...
(a) f(x) - Portal UniMAP
... = 3x2 + 6xΔx + 3(Δx)2 By the first principle, f'(x) = lim {[f(x + Δx) – f(x)]/ Δx} Δx→0 = lim {[3x2 + 6xΔx + 3(Δx)2 – 3x2]/ Δx} ...
... = 3x2 + 6xΔx + 3(Δx)2 By the first principle, f'(x) = lim {[f(x + Δx) – f(x)]/ Δx} Δx→0 = lim {[3x2 + 6xΔx + 3(Δx)2 – 3x2]/ Δx} ...
Derivative of General Exponential and Logarithmic
... To find the derivative of a general exponential function, f (x) = b x where b 6= e, we can a technique similar to that used to find the derivative of f (x) = ln x. ...
... To find the derivative of a general exponential function, f (x) = b x where b 6= e, we can a technique similar to that used to find the derivative of f (x) = ln x. ...
Derivatives and Integrals Involving Inverse Trig Functions
... Calculus II MAT 146 Derivatives and Integrals Involving Inverse Trig Functions As part of a first course in Calculus, you may or may not have learned about derivatives and integrals of inverse trigonometric functions. These notes are intended to review these concepts as we come to rely on this infor ...
... Calculus II MAT 146 Derivatives and Integrals Involving Inverse Trig Functions As part of a first course in Calculus, you may or may not have learned about derivatives and integrals of inverse trigonometric functions. These notes are intended to review these concepts as we come to rely on this infor ...
1 e - Shelton State
... •Because the natural exponential function f(x) = ex is one-to-one, it must have an inverse function. Its inverse is called the natural logarithmic function. The domain of the natural logarithmic function is the set of positive real numbers. ...
... •Because the natural exponential function f(x) = ex is one-to-one, it must have an inverse function. Its inverse is called the natural logarithmic function. The domain of the natural logarithmic function is the set of positive real numbers. ...
Have a great summer! Ponder!
... mathematical terms and in physics terms. For example, the derivative of a displacement function gives you a new function that calculates the slope of the displacement function. In physics terms this new function allows you to calculate instantaneous velocity. You should also be able to go through an ...
... mathematical terms and in physics terms. For example, the derivative of a displacement function gives you a new function that calculates the slope of the displacement function. In physics terms this new function allows you to calculate instantaneous velocity. You should also be able to go through an ...
Lim.B.2
... Limits of sums, differences, products, quotients, and composite functions can be found using the basic theorems of limits and algebraic rules The limit of a function may be found by using algebraic manipulation, alternate forms of trigonometric functions (trig identities), or the squeeze theorem ...
... Limits of sums, differences, products, quotients, and composite functions can be found using the basic theorems of limits and algebraic rules The limit of a function may be found by using algebraic manipulation, alternate forms of trigonometric functions (trig identities), or the squeeze theorem ...
Document
... 21. In period 1, a chicken gives birth to 2 chickens (so, there are three chickens after period 1). In period 2, each chicken born in period 1 either gives birth to 2 chickens or does not give birth to any chicken. If a chicken does not give birth to any chicken in a period, it does not give birth i ...
... 21. In period 1, a chicken gives birth to 2 chickens (so, there are three chickens after period 1). In period 2, each chicken born in period 1 either gives birth to 2 chickens or does not give birth to any chicken. If a chicken does not give birth to any chicken in a period, it does not give birth i ...
MAXIMA AND MINIMA
... The seventeenth-century development of the calculus was strongly motivated by questions concerning extreme values of functions. ...
... The seventeenth-century development of the calculus was strongly motivated by questions concerning extreme values of functions. ...
POWER SERIES
... Let f be continuous on the interval a, b .To find the open intervals on which f is increasing or decreasing, use the following steps. 1. Locate the critical numbers of f x in a, b and use these numbers to determine the test intervals. 2. Determine the sign of f ' x at one test value ...
... Let f be continuous on the interval a, b .To find the open intervals on which f is increasing or decreasing, use the following steps. 1. Locate the critical numbers of f x in a, b and use these numbers to determine the test intervals. 2. Determine the sign of f ' x at one test value ...
Solution
... proceed as in (b) and (c), flipping the first integral and applying the chain rule to both. We ultimately get that ...
... proceed as in (b) and (c), flipping the first integral and applying the chain rule to both. We ultimately get that ...
A function f is linear if f(ax + by) = af(x) + bf(y) Or equivalently f is
... Solve y 00 + 3y 0 + 4y = 0, y(0) = 5, y 0 (0) = 6. 1.) Take the LaPlace Transform of both sides of the ...
... Solve y 00 + 3y 0 + 4y = 0, y(0) = 5, y 0 (0) = 6. 1.) Take the LaPlace Transform of both sides of the ...
Calculus of Several Variables
... Ex. Redo (Ex 1) to find the relative minimum of f (x, y) = 2x2 + y 2 subject to g(x, y) = x + y − 1 = 0. Ex. (HW 12, p.583) Find the maximum and minimum values of f (x, y) = exy subject to the constraint x2 + y 2 = 8. The Method of Lagrange Multipliers can be similarly applied to functions of more v ...
... Ex. Redo (Ex 1) to find the relative minimum of f (x, y) = 2x2 + y 2 subject to g(x, y) = x + y − 1 = 0. Ex. (HW 12, p.583) Find the maximum and minimum values of f (x, y) = exy subject to the constraint x2 + y 2 = 8. The Method of Lagrange Multipliers can be similarly applied to functions of more v ...
Math 1100 Practice Exam 3 23 November, 2011
... 19. Use four rectangles to approximate −1 x2 + x + 1dx. Evaluate at left-hand endpoints to determine the heights of the rectangles. ...
... 19. Use four rectangles to approximate −1 x2 + x + 1dx. Evaluate at left-hand endpoints to determine the heights of the rectangles. ...