"Online calculus bc tutoring" Introduction
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Relation between d y and dy Let A(x, y) and B(x + d x, y + d y) be two neighbouring points on the curve y = f(x). Let dx and dy be the differentiables of x and y respectively. AC = d x = dx BC = d y DC = dy dy = f ' (x) d x d y - dy = BC - CD = BD \ The differential 'dy' and the..
Relation between d y and dy Let A(x, y) and B(x + d x, y + d y) be two neighbouring points on the curve y = f(x). Let dx and dy be the differentiables of x and y respectively. AC = d x = dx BC = d y DC = dy dy = f ' (x) d x d y - dy = BC - CD = BD \ The differential 'dy' and the..Fundamental Theorem of Calculus
The fundamental theorem of calculus is the statement that the two central operations of calculus, differentiation and integration, are inverse operations: if a continuous function is first integrated and then differentiated, the original function is retrieve..
First Fundamental Theorem of Integral Calculus
Let f(x) be a continuous function on the closed interval [a, b]. Let the area function A(x) be defined by th..
Let f(x) be a continuous function on the closed interval [a, b]. Let the area function A(x) be defined by th..Second Fundamental Theorem of Integral Calculus
Let f(x) be a continuous function defined on an interval [a,b]. between the limits a and b. This statement is also known as 'fundamental theorem of calculus'. We call b, the upper limit of x and a, the lower limit. If in place of F(x) we take F(x)+c as the value of the integral, we have =..
Let f(x) be a continuous function defined on an interval [a,b]. between the limits a and b. This statement is also known as 'fundamental theorem of calculus'. We call b, the upper limit of x and a, the lower limit. If in place of F(x) we take F(x)+c as the value of the integral, we have =.. Calculus BC problems for mathBC Calculus Sample Question 1 & 2. In this video, I show how to solve problems 1 & 2 from a sample BC Calculus test. For more free math videos, visit JustMathTutoring.com
Calculus BC 2008 2 a2a of 2008 Calculus BC exam (free response)
Question : Let f be a function having derivatives of all orders for all real numbers. The 3rd degree Taylor polynomial for f about x=2 is given by T(x) = 7-9(x-2)^2-3(x-2)^3.
a)Is there enough infro to determine wheter f has a critical point at x=2? If so determine wheter f(2) is a relative min, max, or neither. explain all.
b) Use T(x) to find an approx for f(0). Is there enough info to determine wheter f has a critical point at x=0? if not explain? if so determine wheter f(0) is a relative max, min, o..
Answer : a) f(2)=7 ; f '(2)=0 ; f ''(2)= -18 ; f '''(2)= -18 it has a critical point in x=2 because f '(2)=0 it is a max because f ''(2)<0
Answer : a) f(2)=7 ; f '(2)=0 ; f ''(2)= -18 ; f '''(2)= -18 it has a critical point in x=2 because f '(2)=0 it is a max because f ''(2)<0
Question : I am confused how to verify equations such as: y=2+e^(-x^3) is a solution of the differential equation y' + 3x^2y=6x^2. Do I differentiate the y equation or do I integrate the implicit equation and then what is the next step?
Answer : I'd do the intergrating factor method on it. y' + 3x^2 y = 6x^2 e^(x^3)y' + 3x^2 e^(x^3) y = 6x^2 e^(x^3) e^(x^3) y = 2e^(x^3) + C y = 2 + C / (e^(x^3) )
Answer : I'd do the intergrating factor method on it. y' + 3x^2 y = 6x^2 e^(x^3)y' + 3x^2 e^(x^3) y = 6x^2 e^(x^3) e^(x^3) y = 2e^(x^3) + C y = 2 + C / (e^(x^3) )