as a POWERPOINT
... change of this function at x = 6? x = -1, x = a? We could do a limit calculation to find the derivative value but we will graph it on the GC and graph its derivative. So the derivative function equation is f `(x) = 0 ...
... change of this function at x = 6? x = -1, x = a? We could do a limit calculation to find the derivative value but we will graph it on the GC and graph its derivative. So the derivative function equation is f `(x) = 0 ...
Math 170 Calculus w/Analytic Geometry I Fall 2015
... epsilon-delta demonstrations of the existence of a limit at a point State the definition of “continuity” and use it to demonstrate the continuity of a function at a point or over an interval Define a derivative and use it to develop rules for calculations of a derivative Calculate one-sided and two- ...
... epsilon-delta demonstrations of the existence of a limit at a point State the definition of “continuity” and use it to demonstrate the continuity of a function at a point or over an interval Define a derivative and use it to develop rules for calculations of a derivative Calculate one-sided and two- ...
Ken`s Cheat Sheet 2014 Version 11 by 17
... f x dx If f is continuous on a, b then at some point c in a, b , f c b a a Rolle’s Theorem “A well behaved function that is not one to one will have a horizontal tangent” If f is continuous on a, b and differentiable on a, b such that f ( a ) f (b) , then there is at least on ...
... f x dx If f is continuous on a, b then at some point c in a, b , f c b a a Rolle’s Theorem “A well behaved function that is not one to one will have a horizontal tangent” If f is continuous on a, b and differentiable on a, b such that f ( a ) f (b) , then there is at least on ...
AP Calculus
... form ln u . When you differentiate functions in the form y ln u do so as if the absolute value were not present. Theorem – Derivative Involving Absolute Value If u is a differentiable function of x such that u Example #6 Find the derivative of f ( x) ...
... form ln u . When you differentiate functions in the form y ln u do so as if the absolute value were not present. Theorem – Derivative Involving Absolute Value If u is a differentiable function of x such that u Example #6 Find the derivative of f ( x) ...
WarmUp: 1) Find the domain and range of the following relation
... Examples: 4) The function h(t) = 1248 160t +16t2 represents the height of an object ejected downward at a rate of 160 feet per second from an airplane flying at 1248 feet. Find each value if t is the number of seconds since the object has ...
... Examples: 4) The function h(t) = 1248 160t +16t2 represents the height of an object ejected downward at a rate of 160 feet per second from an airplane flying at 1248 feet. Find each value if t is the number of seconds since the object has ...
2-18-2002, LECTURE 1. The Lagrange Remainder and Applications
... rigor. The mathematicians of the time felt that the Taylor polynomial would yield something approximately equal to the function in question. Unfortunately, they were incorrect, since this is not always the case.1 The Lagrange Remainder theorem does give one the desired control. Theorem 1.1 (Lagrange ...
... rigor. The mathematicians of the time felt that the Taylor polynomial would yield something approximately equal to the function in question. Unfortunately, they were incorrect, since this is not always the case.1 The Lagrange Remainder theorem does give one the desired control. Theorem 1.1 (Lagrange ...
3.5 Derivatives of Trigonometric Functions
... example of simple harmonic motion. If a weight hanging from a spring is stretched 5 units beyond its resting position (s=0) and released at time t = 0 to bob up and down, its position at any later time t is ...
... example of simple harmonic motion. If a weight hanging from a spring is stretched 5 units beyond its resting position (s=0) and released at time t = 0 to bob up and down, its position at any later time t is ...
The Tangent Line Problem
... The Tangent Line Problem Essentially, the problem of finding the tangent line at a point P boils down to the problem of finding the slope of the tangent line at point P. You can approximate this slope using a secant line through the point of tangency and a second point on the ...
... The Tangent Line Problem Essentially, the problem of finding the tangent line at a point P boils down to the problem of finding the slope of the tangent line at point P. You can approximate this slope using a secant line through the point of tangency and a second point on the ...
Solutions
... help you review important concepts and give you an idea of what kind of questions may be asked (but not the questions themselves!). Instructions: Show all work for full credit. Please do all work in the Blue Books! Refer to any work done on separate pages. You will have 75 minutes to complete this e ...
... help you review important concepts and give you an idea of what kind of questions may be asked (but not the questions themselves!). Instructions: Show all work for full credit. Please do all work in the Blue Books! Refer to any work done on separate pages. You will have 75 minutes to complete this e ...
ANTIDERIVATIVES AND AREAS AND THINGS 1. Integration is
... What we just used to calculate the area under a curve between two points is a big result called The Fundamental Theorem of Calculus and understanding this theorem will be one of our main goals for the course. That said, let’s just go a head and state: Theorem 1 (The Area Theorem). If f is a function ...
... What we just used to calculate the area under a curve between two points is a big result called The Fundamental Theorem of Calculus and understanding this theorem will be one of our main goals for the course. That said, let’s just go a head and state: Theorem 1 (The Area Theorem). If f is a function ...
The Mean Value Theorem Math 120 Calculus I
... Functions with equal derivatives. We can also use the MVT to conclude that if two functions have equal derivatives on an interval, then they differ by a constant. For if f 0 = g 0 , then (f − g)0 = 0, therefore, by the preceding theorem, f − g is constant. This theorem implies that if you know the d ...
... Functions with equal derivatives. We can also use the MVT to conclude that if two functions have equal derivatives on an interval, then they differ by a constant. For if f 0 = g 0 , then (f − g)0 = 0, therefore, by the preceding theorem, f − g is constant. This theorem implies that if you know the d ...
HERE
... function is the slope of its graph, and so it must be negative when x is very small and positive when x is large (or vice-versa if the first term of the polynomial is negative). This means that the derivative of an even polynomial function cannot be even. A similar argument shows that the derivative ...
... function is the slope of its graph, and so it must be negative when x is very small and positive when x is large (or vice-versa if the first term of the polynomial is negative). This means that the derivative of an even polynomial function cannot be even. A similar argument shows that the derivative ...
Lecture 18: Taylor`s approximation revisited Some time ago, we
... The expression in the Theorem, f (c) + f 0 (c)(x − c) + . . . + f n!(c) (x − c)n is referred to as the Taylor polynomial of f at c. It is, of course, a polynomial of degree n which approximates f at c. We know that the error is o((x − c)n ) so that it is getting small quite fast as x approaches c. B ...
... The expression in the Theorem, f (c) + f 0 (c)(x − c) + . . . + f n!(c) (x − c)n is referred to as the Taylor polynomial of f at c. It is, of course, a polynomial of degree n which approximates f at c. We know that the error is o((x − c)n ) so that it is getting small quite fast as x approaches c. B ...
AP Calculus AB - Review for AP Calculus AB Exam (2009).
... taking the derivative more difficult - Remember: anytime you take a derivative of a function with y, dy you must put after that term dx dy - Then solve the resulting equation for dx ** Don’t forget about PRODUCT RULE on these problems! Example Problem: Find ...
... taking the derivative more difficult - Remember: anytime you take a derivative of a function with y, dy you must put after that term dx dy - Then solve the resulting equation for dx ** Don’t forget about PRODUCT RULE on these problems! Example Problem: Find ...
2.1 Functions
... A relation is a set of ordered pairs. The set of all first coordinates is called the domain of the relation. The set of all second coordinates is called the range of the relation. A relation is a function if each element of the domain is paired with exactly (only) one element of the range. (Every x- ...
... A relation is a set of ordered pairs. The set of all first coordinates is called the domain of the relation. The set of all second coordinates is called the range of the relation. A relation is a function if each element of the domain is paired with exactly (only) one element of the range. (Every x- ...
Norm and Derivatives
... differentiable function x. In application to find Frechet or Hadamard derivative generally we shout try first to determine the form of derivative deducing Gateaux derivative acting on h,df(h) for a collection of directions h which span B1. This reduces to computing the ordinary derivative (with resp ...
... differentiable function x. In application to find Frechet or Hadamard derivative generally we shout try first to determine the form of derivative deducing Gateaux derivative acting on h,df(h) for a collection of directions h which span B1. This reduces to computing the ordinary derivative (with resp ...
Solutions - Penn Math
... C(y) is a constant. Any choice of constant will give us a potential function, so we may as well choose the constant to be zero. Thus a potential function is f (x, y) = x3 y 2 + ex . R The fundamental theorem of line integrals says that C F · dr = f (b) − f (a), where a is the starting point of the c ...
... C(y) is a constant. Any choice of constant will give us a potential function, so we may as well choose the constant to be zero. Thus a potential function is f (x, y) = x3 y 2 + ex . R The fundamental theorem of line integrals says that C F · dr = f (b) − f (a), where a is the starting point of the c ...
Solution - Math TAMU
... asymptotes when x = ±1, and the x-axis is a horizontal asymptote when x → ±∞. In order for the graph to have negative slope everywhere on its domain and to have the origin as its only inflection point, the graph must look something like the following figure. ...
... asymptotes when x = ±1, and the x-axis is a horizontal asymptote when x → ±∞. In order for the graph to have negative slope everywhere on its domain and to have the origin as its only inflection point, the graph must look something like the following figure. ...
SOLUTIONS TO PROBLEM SET 4 1. Without loss of generality
... To show the Feller property take an arbitrary f ∈ C0 (R+ ), i.e. a continuous function on R+ which vanishes at ∞. Then, g : R 7→ R defined by g(x) = f (|x|) belongs to C0 (R). Note that Qt f (x) = Pt g(x), x ≥ 0. Thus, the desired Feller property follows from the Feller property of Brownian motion. ...
... To show the Feller property take an arbitrary f ∈ C0 (R+ ), i.e. a continuous function on R+ which vanishes at ∞. Then, g : R 7→ R defined by g(x) = f (|x|) belongs to C0 (R). Note that Qt f (x) = Pt g(x), x ≥ 0. Thus, the desired Feller property follows from the Feller property of Brownian motion. ...
Math 125 – Section 02
... arithmetic) to get the answer, explain what you did and why you did it. Point values for each part are given in brackets. [22 total] NO WORK = NO CREDIT!! Answer the following TRUE/FALSE questions. Defend your answer, if it is true, explain why, if it is false, give an example showing that it is fal ...
... arithmetic) to get the answer, explain what you did and why you did it. Point values for each part are given in brackets. [22 total] NO WORK = NO CREDIT!! Answer the following TRUE/FALSE questions. Defend your answer, if it is true, explain why, if it is false, give an example showing that it is fal ...