Notes
... firework at a starting height of 610 ft with and initial upward velocity of 88 ft/s. How long will it take for the start to reach it’s maximum height? How far above the ground will it be? **Use the falling object function: h = -16t² + v 0 + h 0 ; where v 0 is initial velocity and h 0 is the initial ...
... firework at a starting height of 610 ft with and initial upward velocity of 88 ft/s. How long will it take for the start to reach it’s maximum height? How far above the ground will it be? **Use the falling object function: h = -16t² + v 0 + h 0 ; where v 0 is initial velocity and h 0 is the initial ...
Kilgo Lesson Plan format
... Students will continue to use the Fundamental Theorem of Calculus. Engage and connect Derivative practice Guided instruction – We will practice using a worksheet from a Rice institute on Fundamental Theorem of Calculus This worksheet focuses on AP style questions that ask the student to use the ...
... Students will continue to use the Fundamental Theorem of Calculus. Engage and connect Derivative practice Guided instruction – We will practice using a worksheet from a Rice institute on Fundamental Theorem of Calculus This worksheet focuses on AP style questions that ask the student to use the ...
Lecture notes 2.26.14
... Today we will recapitulate basic definitions and properties from multivariate calculus which we will need in the coming lectures about Convex Optimization. ...
... Today we will recapitulate basic definitions and properties from multivariate calculus which we will need in the coming lectures about Convex Optimization. ...
Objective (Defn): something that one`s efforts or actions are intended
... 103. State the definition of a geometric series, and the specific conditions under which such a series either converges or diverges. Determine whether or not a given geometric series, or series which can be readily transformed into one, converges. 104. Describe generally the purpose of convergence t ...
... 103. State the definition of a geometric series, and the specific conditions under which such a series either converges or diverges. Determine whether or not a given geometric series, or series which can be readily transformed into one, converges. 104. Describe generally the purpose of convergence t ...
Tutorial Sheet 9 Topics: Differentiating Trigonometric Functions +
... 8. For the functions in parts (a) and (b) in the previous question, find any points of inflection. 9. For each of the following polynomials, (i) Find all critical points, (ii) Classify each critical point as a local maximum, local minimum, or neither, (iii) Find all points of inflection, (iv) Find t ...
... 8. For the functions in parts (a) and (b) in the previous question, find any points of inflection. 9. For each of the following polynomials, (i) Find all critical points, (ii) Classify each critical point as a local maximum, local minimum, or neither, (iii) Find all points of inflection, (iv) Find t ...
9 Complex-valued Functions
... As a mathematical term, “function” was coined by Gottfried Leibniz, in a 1673 letter, to describe a quantity related to a curve, such as a curve’s slope at a specific point. In fact, the functions Leibniz considered are today called differentiable functions, which are the basis of calculus. In the I ...
... As a mathematical term, “function” was coined by Gottfried Leibniz, in a 1673 letter, to describe a quantity related to a curve, such as a curve’s slope at a specific point. In fact, the functions Leibniz considered are today called differentiable functions, which are the basis of calculus. In the I ...
Solutions
... 1. Suppose a stone is thrown vertically upward from the edge of a cliff with initial velocity 64 ft/s from a height of 32 ft above the ground. The height h (in ft) of the stone above the ground t seconds after it is thrown is h = −16t2 + 64t + 32. (a) Determine the velocity v of the stone after t se ...
... 1. Suppose a stone is thrown vertically upward from the edge of a cliff with initial velocity 64 ft/s from a height of 32 ft above the ground. The height h (in ft) of the stone above the ground t seconds after it is thrown is h = −16t2 + 64t + 32. (a) Determine the velocity v of the stone after t se ...
Notes - Ryan, Susan
... version of F(x) by evaluating the definite integral. Once you find F(x), find its derivative F’(x). What do you notice? ...
... version of F(x) by evaluating the definite integral. Once you find F(x), find its derivative F’(x). What do you notice? ...
Math 111- Solution of Test 4 Problem 1. Find the antiderivative F of
... (3) On what intervals is f concave up? concave down? Justify your answers to receive credit. (4) For what values of x does f have an inflection point? Justify your answers. ISolution: From the graph of the derivative f 0 , we have the following sign chart of f 0 (positive if above the x-axis and neg ...
... (3) On what intervals is f concave up? concave down? Justify your answers to receive credit. (4) For what values of x does f have an inflection point? Justify your answers. ISolution: From the graph of the derivative f 0 , we have the following sign chart of f 0 (positive if above the x-axis and neg ...
Solutions to modeling with functions
... The goal of this project is to practice writing functions that model given situations. Each of the functions you create should depend on only one variable. You’ll need this skill to solve applied optimization problems. 1. The product of two numbers n and m is 100, and n must be positive. (For exampl ...
... The goal of this project is to practice writing functions that model given situations. Each of the functions you create should depend on only one variable. You’ll need this skill to solve applied optimization problems. 1. The product of two numbers n and m is 100, and n must be positive. (For exampl ...
PROOF OF THE TRAPEZOID SUM ERROR ESTIMATE Math 112
... Monotonicity and the Speed Limit Law. If you took Math 111 using the text by Ostebee & Zorn, you saw a property of derivatives they call the Speed Limit Law: If F : [a, b] → R is differentiable and F (x) ≤ K for all x in [a, b], then F (b) − F (a) ≤ K(b − a). If F is non-negative and we think of ...
... Monotonicity and the Speed Limit Law. If you took Math 111 using the text by Ostebee & Zorn, you saw a property of derivatives they call the Speed Limit Law: If F : [a, b] → R is differentiable and F (x) ≤ K for all x in [a, b], then F (b) − F (a) ≤ K(b − a). If F is non-negative and we think of ...
MATHEMATICS 2030
... derivatives), directional derivatives, gradient, higher partial derivatives and Clairaut’s Theorem, optimization (maxima and minima) c. Vector fields, gradient (conservative) vector fields, conditions for conservativity over domains in R2 and R3, calculation of the primitives of a conservative vecto ...
... derivatives), directional derivatives, gradient, higher partial derivatives and Clairaut’s Theorem, optimization (maxima and minima) c. Vector fields, gradient (conservative) vector fields, conditions for conservativity over domains in R2 and R3, calculation of the primitives of a conservative vecto ...
Quadratic functions One of the simplest kinds of functions that exhibit
... easily solved: since a product equals zero only when one of the€factors is zero, and a ≠ 0, we must have that either x − r = 0 or x − s = 0 ...
... easily solved: since a product equals zero only when one of the€factors is zero, and a ≠ 0, we must have that either x − r = 0 or x − s = 0 ...
∞ ∞ lnx sinx x =1 Local minimum
... Be able to determine the behavior of a function f given the graph of its derivative f' (WeBWorK 1). Know the Concavity Test: f ' '0 ⇒ f is concave up f ' '0 ⇒ f is concave down Know the definition of an inflection point ( a point on the graph of f where the concavity changes) and how to find it (i ...
... Be able to determine the behavior of a function f given the graph of its derivative f' (WeBWorK 1). Know the Concavity Test: f ' '0 ⇒ f is concave up f ' '0 ⇒ f is concave down Know the definition of an inflection point ( a point on the graph of f where the concavity changes) and how to find it (i ...
Sec 3.1
... Objective 5: Determining the Domain of a Function Given the Equation The domain of a function y f ( x) is the set of all values of x for which the function is defined. It is very helpful to classify a function to determine its domain. ...
... Objective 5: Determining the Domain of a Function Given the Equation The domain of a function y f ( x) is the set of all values of x for which the function is defined. It is very helpful to classify a function to determine its domain. ...
chapter1
... Combining Functions We can combine functions in any of five ways. Four of these are the familiar arithmetic operations; addition, subtraction, multiplication and division, and are very intuitive. The fifth type of combining functions is called composition of functions. In all cases, we’ll be intere ...
... Combining Functions We can combine functions in any of five ways. Four of these are the familiar arithmetic operations; addition, subtraction, multiplication and division, and are very intuitive. The fifth type of combining functions is called composition of functions. In all cases, we’ll be intere ...
Section 6.3, Question 41: Suppose that the marginal cost function of
... Section 6.3, Question 41: Suppose that the marginal cost function of a handbag manufac3 2 turer is C 0 (x) = 32 x − x + 200 dollars per unit at production level x, where x is measured in units of 100 handbags). (a) Find the total cost of producing 6 additional units if 2 units are currently being pr ...
... Section 6.3, Question 41: Suppose that the marginal cost function of a handbag manufac3 2 turer is C 0 (x) = 32 x − x + 200 dollars per unit at production level x, where x is measured in units of 100 handbags). (a) Find the total cost of producing 6 additional units if 2 units are currently being pr ...
ECO4112F Section 4 Integration
... at this point, certain mathematic tools are required for dynamic analysis, such as integration and differential equations. Without these tools, it becomes impossible to consider problems which are not static in nature. We will be covering both of these topics in a mainly mathematical way, leaving ec ...
... at this point, certain mathematic tools are required for dynamic analysis, such as integration and differential equations. Without these tools, it becomes impossible to consider problems which are not static in nature. We will be covering both of these topics in a mainly mathematical way, leaving ec ...
Taylor Polynomials: The Lagrange Error Bound
... show that the Taylor polynomials for f approximate f uniformly well on intervals of the form [−h, h]. What is more, a similar inequality holds for the Taylor polynomials for f 0 , and so those polynomials approximate f 0 uniformly well on intervals of the form [−h, h]. Thus, the calculus of the Tayl ...
... show that the Taylor polynomials for f approximate f uniformly well on intervals of the form [−h, h]. What is more, a similar inequality holds for the Taylor polynomials for f 0 , and so those polynomials approximate f 0 uniformly well on intervals of the form [−h, h]. Thus, the calculus of the Tayl ...
06.01-text.pdf
... ş 2. When we write cos x dx “ sin x ` C, the content of this mathematical statement can be phrased in terms of antiderivatives (as in Question 1). But it can also be phrased in terms of derivatives: ”Functions of the form sin x ` C have, as their derivative, the function cos x.” When viewed this way ...
... ş 2. When we write cos x dx “ sin x ` C, the content of this mathematical statement can be phrased in terms of antiderivatives (as in Question 1). But it can also be phrased in terms of derivatives: ”Functions of the form sin x ` C have, as their derivative, the function cos x.” When viewed this way ...
Derivatives of Exponential, Logarithmic and Trigonometric
... 5. The concentration of pollutants (in grams per liter) in a river is approximated by C(x) = .04e−4x where x is the number of miles downstream from a place where the measurements are taken. (a) Determine the initial pollution and the pollution 2 miles downstream. (b) Determine how much the concentr ...
... 5. The concentration of pollutants (in grams per liter) in a river is approximated by C(x) = .04e−4x where x is the number of miles downstream from a place where the measurements are taken. (a) Determine the initial pollution and the pollution 2 miles downstream. (b) Determine how much the concentr ...