*Several examples with detailed solutions are presented.*3-Dimensional graphs of functions are shown to confirm the existence of these points. Several tables of mathematical formulas including decimal multipliers, series, factorial, permutations, combinations, binomial expansion, trigonometric formulas and tables of derivatives, integrals, Laplace and Fourier transforms.

*Several examples with detailed solutions are presented.*3-Dimensional graphs of functions are shown to confirm the existence of these points. Several tables of mathematical formulas including decimal multipliers, series, factorial, permutations, combinations, binomial expansion, trigonometric formulas and tables of derivatives, integrals, Laplace and Fourier transforms.

The main result of this section, the fundamental theorem of calculus, includes a very important formula for evaluating integrals.

This theorem shows us how to evaluate integrals by first evaluating antiderivatives.

Several examples, with detailed solutions, involving products, sums and quotients of exponential functions are examined. Examples of the derivatives of logarithmic functions, in calculus, are presented.

Several examples, with detailed solutions, involving products, sums and quotients of exponential functions are examined. Newton's method is an example of how differentiation is used to find zeros of functions and solve equations numerically.

When graphing a solution of an equation in calculus, such as example 1, the graph will pass through the y-value 4/3 when x is the value 1.

The line will be a straight line and the graph is said to be continuous at x = 1.We shall verify a special case of this theorem at the end of this section. Example 1 The following theorem is called the fundamental theorem and is a consequence of Theorem 1 .The Fundamental Theorem of Calculus Let f be continuous on [a. Then, To verify the fundamental theorem, let F be given by , as in Formula (1). Since G is also an antiderivative of f, we know that there is a constant c for which F(x} = G(x) c.b ], and suppose G is any antiderivative of f on [a, b], that is. Since F(a) = J;' f(x) dx = 0, it follows that 0 = F (a) = G (a) c and hence c = -G(a).Thus, F(x) = G(x) c = G(x) - G(a), from which we see that For convenience, we introduce the following notation: With this notation, Formula (4) can be written as The following equivalent formula demonstrates the convenience of using a symbol for the integral that resembles the one for the antiderivative.Examples with detailed solutions on how to use Newton s method are presented. Linear approximation is another example of how differentiation is used to approximate functions by linear ones close to a given point.Examples with detailed solutions on linear approximations are presented. Locate relative maxima, minima and saddle points of functions of two variables.The concept of limits is to evaluate a function as x approaches a value but never takes on that value.To solve a limit, see the 4 examples of a limit problems involving direct substitution.To find the a complex function limit is needed with the help of limits a complex function can be broken into small pieces. After learning concepts again check your self whether you understand the concept or not.Solve all the small parts of the function and add it. Go through your math tutor notes make sure you understand each step, if not then ask help from the teacher. Practice is the key of success, practice all example problem and worksheet.2.

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