Summary
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 =..Introduction
Differential calculus can be considered as mathematics of motion, growth and change where there is a motion, growth, change. Whenever there is variable forces producing acceleration, differential calculus is the right mathematics to appl..
Differentiation
Introduction - The derivative, measures the rate at which the dependent variable changes with respect to the independent variable. It is one of the most important ideas in Calculus. The differentiation of functions are widely used in science, economics, medicine and computer scienc..
Introduction to Differentiation
After having studied functions, limits and continuity in the previous chapter, we shall further divide the class of continuous functions into two sub classes, derivable and non-derivable.After having studied functions, limits and continuity in the previous chapter, we shall further divide the class..
Introduction
Let us began this chapter with the following statement: Often a physician may want to test how small changes in dosage can affect the body's response to a particular drug. An economist may want to study how investment changes with variation in interest rates. How the velocity of a heavy meteorite e..
Note:
From the above two theorem, we infer the following (Anti derivative of the function f(x) at b) - (Anti derivative of the function f(x) at a) (ii) The fundamental theorem of integral calculus shows a close relationship between differentiation and integration (iii) These theorems give an..
From the above two theorem, we infer the following (Anti derivative of the function f(x) at b) - (Anti derivative of the function f(x) at a) (ii) The fundamental theorem of integral calculus shows a close relationship between differentiation and integration (iii) These theorems give an..Area function
We have already defined, for a continuous function f(x) on a closed interval [a, b] as the area of the region bounded by the curve y = f(x), X-axis and x= a and x = b. In other words, area of the shaded region is a function of x. The function A(x) is shown in figure below. This area function A(x) i..
We have already defined, for a continuous function f(x) on a closed interval [a, b] as the area of the region bounded by the curve y = f(x), X-axis and x= a and x = b. In other words, area of the shaded region is a function of x. The function A(x) is shown in figure below. This area function A(x) i..See what our Users say :
I really liked this tutoring. Helped me alot and gave me more ways to work a problem. awesome help and I even got the idea on these problems - kimi
The tutor remembered me from last week and noted my improvement. This is simply amazing :)
My son started joined Tutor Vista in 6 th grade, Now he is 8 th grade, He likes Tutor Vista tutors more than his school teachers…Lucy
I have experienced very innovative way of learning, I joined online tutoring at Tutorvista few months back when I was in grade 10, I scored really well in grade 10 and ny parents were really happy.
Looking for More Help!
