calculus word problems

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..

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..

The degree of a differential equation is the highest power of the highest order derivative after making the equation free from radicals and fractional indices as far as the derivatives are concerned. In other words, the degree of a differential equation whose terms are polynomial in the ..

So far, we know how to differentiate functions like sin x and x 3 - 5. But how do we differentiate a function of a function? That is how can we differentiate sin (x 3 - 5)?So far, we know how to differentiate functions like sin x and x 3 - 5. But how do we differentiate a function of a function? Th..

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 ..

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 ..

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..

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 ..

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..

Let f(x) be a continuous function on the closed interval [a, b]. Let the area function A(x) be defined by th..