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Integration
We have, so far, seen that differential calculus measures the rate of change of functions. Differentiation is the process of finding the derivative (rate of change) of a function F(x) and is denoted by F'(x) Often, we may know the rate of change, F'(x) of a function F(x) which is unknown to us. In such situations we would like to find out the original function F(x) from the derivative, F'(x). Reversing the process of differentiation and finding out the original function from the derivative is called integration. The original function, F(x) is called the integral.
The left hand side of the equation is read as "the indefinite integral of f(x) with respect to x. The symbol is the integral sign, f(x) is the integrand and 'c' is an arbitrary constant. The arbitrary constant 'c' is added because of the following reason:
If d/dx {F(x)} = f(x) then we can also write that d/dx {F(x) + c} = f(x) where 'c' is an arbitrary constant, because the derivative of any constant is zero.
The Definition of the Limit In this section we will look at the precise, mathematical definition of three types of limits we'll be looking at the precise definition of limits
Question: All rates should be calculated to 3 decimal places in % (e.g. 1.234%), the discount factors to 5 decimal places (e.g. 0.98765), and the bond prices to 3 decimal place
please can you help me with word problems
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A motor boat takes Six hours to cover 100 km downstream and 30 km upstream. If the motor boat goes 75 km downstream and returns back to its starting point in 8 hours, find the sp
Classify models based on the degree of their abstraction, and provide some examples of such models.
Q. Define Combined Functions? Ans. We are often interested in functions which combine a trigonometric function with another type of function. For example, y = x + sinx wi
solve the recurrence relation an=2an-1+n, a0=1
For the initial value problem y' + 2y = 2 - e -4t , y(0) = 1 By using Euler's Method along with a step size of h = 0.1 to get approximate values of the solution at t = 0.1, 0
How to calculate costs if you have a computerised payroll package for your large business?
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