Rate of Change of Quantity
If a quantity y varies with respect to another quantity 'x' satisfying some rule y = f(x), in other words if y is a function x, then represents the rate of change of y with respect to..
If a quantity y varies with respect to another quantity 'x' satisfying some rule y = f(x), in other words if y is a function x, then represents the rate of change of y with respect to..Integration by parts
In words: Integral of the product of two functions If the integrand is the product of two functions of different types then their order is determined by the word ILATE where I = Inverse trigonometric L = Logarithmic A = Algebraic, T = Trigonometric, E = Exponential In t..
In words: Integral of the product of two functions If the integrand is the product of two functions of different types then their order is determined by the word ILATE where I = Inverse trigonometric L = Logarithmic A = Algebraic, T = Trigonometric, E = Exponential In t..Rate of Change of Quantity
If a quantity y varies with respect to another quantity 'x' satisfying some rule y = f(x), in other words if y is a function x, then represents the rate of change of y with respect to x For x = x 0 , dy/dx at x 0 is called the rate of change of y with respect to x at x 0 . If y is a funct..
If a quantity y varies with respect to another quantity 'x' satisfying some rule y = f(x), in other words if y is a function x, then represents the rate of change of y with respect to x For x = x 0 , dy/dx at x 0 is called the rate of change of y with respect to x at x 0 . If y is a funct..Definition 8:
The first-order first-degree differential equation is said to be homogeneous, if f is a homogeneous function of degree zero, , In other words, f instead of depending on x and y separately, depends on . Thus..
The first-order first-degree differential equation is said to be homogeneous, if f is a homogeneous function of degree zero, , In other words, f instead of depending on x and y separately, depends on . Thus..Improper rational function
If the degree of the numerator is greater than the degree of the denominator in a rational fraction, then the rational function is called improper rational function. Like the case of improper fractions reducible to an integer added to a proper fraction, improper rational function can be reduced as ..
If the degree of the numerator is greater than the degree of the denominator in a rational fraction, then the rational function is called improper rational function. Like the case of improper fractions reducible to an integer added to a proper fraction, improper rational function can be reduced as ..Note:
The word 'primitive' has been used both in reference to a differential equation, and in reference to a function, but there should be no confusion. By a primitive of a given function , we mean a function , such that g'(x) = f(x) for all x R. In other words, y = g(x), (x I) is ..
The word 'primitive' has been used both in reference to a differential equation, and in reference to a function, but there should be no confusion. By a primitive of a given function , we mean a function , such that g'(x) = f(x) for all x R. In other words, y = g(x), (x I) is ..Indefinite Integrals as Antiderivative
Consider the following example: Let f(x) = cos 3x, let us find a function F(x) such that We know that Here In other words we say the integral cos 3x is Suppose then also we ha..
Consider the following example: Let f(x) = cos 3x, let us find a function F(x) such that We know that Here In other words we say the integral cos 3x is Suppose then also we ha..Introduction Exponential and Logarithmic Series
We know that log 2 8 is the number to which 2 must be raised to get 8. Therefore, log 2 8 = 3. In general, if a x = y, (a > 0), then we say that log a y = x. If e x = y, then we say that the natural logarithm of y is x and we write log y = x. In other words, if the base of a logarithm ..
We know that log 2 8 is the number to which 2 must be raised to get 8. Therefore, log 2 8 = 3. In general, if a x = y, (a > 0), then we say that log a y = x. If e x = y, then we say that the natural logarithm of y is x and we write log y = x. In other words, if the base of a logarithm ..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..See what our Users say :
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