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Calculus...The **Calculus** In its existence and approach, **Calculus** attempts to explore the grounds for the undefined nature of a function and designates a sensible understanding about up to which extent it would exist considering assumptions or applicable conditions. As in the rest of the significant fields in Mathematics, **Calculus** intellectuals had professed to work with a base knowledge of other math areas such as algebra and trigonometry to lay foundations and build on definitions, postulates, and theorems in conveying the purpose of the course and attain to its end thereafter. During elementary level of math education, one merely learns that divisibility by zero is not in any way valid or possible...

2 Pages(500 words)Essay

Pre Calculus Mod 5...?Pre-**Calculus** Module 5 Number Basic applicable rules If f(x) = ex, then f '(x) = ex 2) If f(x) = eg(x), then f '(x) = g'(x).eg(x) 3) If f(x) = ln x, then f '(x) = 1/x (x > 0) 4) If f(x) = ln g(x), then f '(x) = g'(x)/g(x) [g(x) > 0] (Tan, 2012). 1. Find the derivatives for the following functions. a. f(X) =100e10x f ' (x) = 1000 e10x b. f(X) = e (10X-5) Let u = 10x – 5 and y = eu Using chain rule to obtain the derivative of the function, f '(x) = (dy / du) (du / dx) dy / du = eu du / dx = 10 f '(x) = (e u)(10) = 10 e u Substituting u = 10x – 5 into the equation, f '(x) = 10 e (10x – 5) c. f(X) =ex3 f '(x) = 3x2 ex3 d. f(X) =2X2 e (1-X2) r (x) = 2x2, r' (x) = 4x s(x) = e (1-X2) s' (x) = -2 e (1-X2) Applying product...

5 Pages(1250 words)Assignment

Calculus and Infinit...?**Calculus** Table of Contents 1.Newton’s and Leibnitz’s approach to **Calculus** (Fluxions and infinitesimals) 3 2. 2.The controversy between Newton and Leibnitz 4 3. 3.The concept of hyper real numbers introduced by Robinson 5 4. 4.Response to criticism of Berkley’s and Marx 6 1. Newton’s and Leibnitz’s approach to **Calculus** (Fluxions and infinitesimals) The infinitesimals have been very crucial in the history of analysis. Initially, Newton and Leibniz used it in developing **calculus**. However, it was challenged by derision issues and finally withdrawn by the establishment of the concept of limit and epsilon-delta definitions during the 1970s. The latter are still in place up to...

5 Pages(1250 words)Essay

Honors program: calculus...Personal Essay What can be more helpful and useful in real life than **calculus** It helps us to understand the paths and the motions of our universe.It helps us to understand the velocity of cars and the movement of molecules. I want to study in the Honors **Calculus** Program because it will give me an opportunity to improve my analytical skills and help me to solve problems in my field. I want to learn advanced analytical methods to solve real-life problems. I am interested in theory as well as applications. I believe that I will be very successful in the program.
I am from Moscow, Russia, and my major is chemical engineering. I know mathematics is important for many academic fields. Sir Isaac Newton...

2 Pages(500 words)Essay

Pre-Calculus...Pre-**Calculus** Opposite (5) hypotenuse 89) Adjacent (8) X = Arctan =(opposite/adjacent) = 5/8, but cotx = 1/tanx
So cot(actan) =8/5
X = arcsin (opposite/hypotenuse) =(-√2/2), but secx = 1/sinx, hence sec(arcsin -√2/2) = -2/√2
2.
The value of the following without using calculator,
a. tan-1(-√3/3).
Let x = tan-1(-√3/3) = tan-1(-√3/3)x√3, hence tanx =-1/√3-3, tan2x=1/3√3, but 1+tan2x=sec2x, thus sec2x=1+1/3 =4/3, secx=1/cosx=2/(√3-3√3), but cos√3+ or -√3-3/2, which can be written as cosx = (√3-3)/2√3, hence x=π/6. From the quadrant, cosine is negative only on 2nd and 3rd , so the solution for will be in quadrants where tan is negative 2rd and 4th, so solutions are 11 π/6 and 5 π/6.
b. cos-1(1), from the quadrant the...

1 Pages(250 words)Speech or Presentation

Pre Calculus...Pre **Calculus** Part 1. The Product Rule Solutions The derivative of f(x) = g(x) h(x) is given by f (x) = g(x)h (x) + h(x) g (x) (Larson, 2012).
a. f(X) = (7X + X-1)*(3X + X2)
Let g(x) = (7X + X-1) and h(X) = (3X + X2)
Therefore, f (X) = (7X + X-1) (3 + 2X) + (3X + X2) (7 -X-2) =
21x + 14x2 + 3x-1 + 2 + 21x – 3x -2 + 7x2 – 1
f (X) = 42x + 21x2 +3x-1 -3x -2 +1
b. . f(X) = (X0.5)*(5-X)
Let g(x) = (X0.5) and h(x) = (5-x)
f (x) = (x1/2) (1) + (5-x) (1/2x -1/2)
f (x) = x1/2 + 2.5x -1/2 – x3/2
c. f(X) = (X3 + X4)*(50 + X2)
Let g(x) = (X3 + X4) and h(x) = (50+x2)
Therefore, f (X) = (X3 + X4) (2x) + (50 + x2) (3x2 + 4x3) =
2x4 + 2x5 + 150x2 + 200x3 + 3x4 +4x5
f (X) = 5 x4 + 6 x5 + 150x2 + 200x3
2. Use the Chain Rule to find...

2 Pages(500 words)Assignment

Calculus Concepts...**Calculus** ID **Calculus** Functions can be expressed as implicit or explicit based on the arrangement of the dependent and independent variables. For a function to be termed as explicit, it is usually given in terms of the independent variables. For instance, say a function y = f(x). It can be seen explicitly that y is the dependent variable and x variable is the independent variable. This means that y is the subject of the formula. The value of y is dependent on the values of x. On the other hand, implicit functions are usually expressed as the dependent and independent variable. For instance, a function y +3x +2 = 0 is expressed with both dependent and independent variables. Although implicit functions can...

3 Pages(750 words)Assignment

Calculus...Introduction The birth of **Calculus**, in the 17th Century, is attributed to Sir Isaac Newton and Gottfried Wilheim von Leibniz. Even though they are the primary founding fathers of **Calculus**, they developed it independently and perceived the fundamental concepts in contrasting manners. For instance, Newton perceived the applications of **Calculus** as being geometrical and having a strong link to the physical world. He even used **Calculus** to try to explain how planets orbit around the sun. On the other hand, according to Leibniz, **Calculus** entailed analyzing the changes in graphs (Simmons 67).
Newton-Leibnitz Controversy
Their professional backgrounds played a...

2 Pages(500 words)Coursework

History of Calculus...of the Mathematics of the Concerned 24 March History of **Calculus** It is indeed true that the discovery of **calculus** does happen to be one of the amazing and praiseworthy things facilitated by human thought and intellect. The history of **calculus** well illustrates its gradual progression from Realist thinking that had its flaws and lacunas to Nominalist thinking that evinced an immense power as far as the solving of the problems of **calculus** is concerned. While delving on the history of **calculus**, the thing that needs to be noticed is that the history of **calculus** is affiliated to varied phases and steps.
The onus for the discovery of...

2 Pages(500 words)Essay

Key concepts of calculus...Key Concepts of **Calculus** is the mathematical way of writing that a function of x approaches a value L when x approaches a value a. For example, if , we can say that which is apparent from the table below
x
f(x)
x
f(x)
9
0.111111111
10.1
0.099009901
9.9
0.101010101
10.01
0.0999001
9.99
0.1001001
10.001
0.099990001
9.999
0.100010001
10.0001
0.099999
9.9999
0.100001
10.0001
0.099999
9.99999
0.1000001
10.00001
0.0999999
9.999999
0.10000001
10.000001
0.09999999
9.9999999
0.100000001
10.0000001
0.099999999
9.999999999
0.1
10.00000001
0.1
10
0.1
10
0.1
The closer x becomes to 10, the closer the f(x) becomes to 0.1 and here this is bidirectional
Yes it is possible for this to be true in case as is evident from where although ...

2 Pages(500 words)Essay