The Fuzzy Logic is discussed with three simple example problems all solved in MATLAB
1. Restaurant Problem
2. Temperature Controller
3. Washing Machine Problem
The Fuzzy Logic is discussed with three simple example problems all solved in MATLAB
1. Restaurant Problem
2. Temperature Controller
3. Washing Machine Problem
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
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Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
5. 5
The Natural Exponential Function
The function f(x) = ln x is increasing on its entire domain,
and therefore it has an inverse function f –1.
The domain of f –1 is the set of all reals, and the range is the
set of positive reals, as shown in Figure 5.19.
Figure 5.19
6. 6
The Natural Exponential Function
So, for any real number x,
If x happens to be rational, then
Because the natural logarithmic function is one-to-one, you
can conclude that f –1(x) and ex agree for rational values of x.
7. 7
The Natural Exponential Function
The following definition extends the meaning of ex to include
all real values of x.
The inverse relationship between the natural logarithmic
function and the natural exponential function can be
summarized as follows.
8. 8
Example 1 – Solving Exponential Equations
Solve 7 = ex + 1.
Solution:
You can convert from exponential form to logarithmic form
by taking the natural logarithm of each side of the equation.
So, the solution is –1 + ln 7 ≈ –0.946. You can check this
solution as shown.
9. 9
Example 1 – Solving Exponential Equations
Solve 7 = ex + 1.
Solution:
You can convert from exponential form to logarithmic form
by taking the natural logarithm of each side of the equation.
So, the solution is –1 + ln 7 ≈ –0.946.
10. 10
Example 1 – Solution (cont)
You can check this solution as shown.
11. 11
The Natural Exponential Function
The familiar rules for operating with rational exponents can
be extended to the natural exponential function, as shown in
the next theorem.
12. 12
The Natural Exponential Function
An inverse function f –1 shares many properties with f.
So, the natural exponential function inherits the following
properties from the natural logarithmic function.
15. 15
Derivatives of Exponential Functions
One of the most intriguing (and useful) characteristics of
the natural exponential function is that it is its own
derivative.
In other words, it is a solution to the differential equation
y' = y. This result is stated in the next theorem.
16. 16
Example 3 – Differentiating Exponential Functions
Find the derivative of each function.
a. y = e2x-1 b. y = e-3/x
Solution:
