Скачать или смотреть || Thomas Calculus 12th & 13th edition exercise # 3.2 Question # 13-16 || Derivative & slope tangent

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slope of tangent:
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The slope of a curve y = f(x) at the point P means the slope of the tangent at the point P. We need to find this slope to solve many applications since it tells us the rate of change at a particular instant. [We write y = f(x) on the curve since y is a function of x. That is, as x varies, y varies also.
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|| Thomas Calculus 12th & 13th edition exercise # 3.2 Question # 01-06 || Derivative by definition||
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The Definition Of The Derivative?
Ans:
In the first section of the Limits chapter we saw that the computation of the slope of a tangent line, the instantaneous rate of change of a function, and the instantaneous velocity of an object at x=a all required us to compute the following limit.


limx
→a

f
(
x
)
−
f
(
a
)
x
−
a
OR


derivative, in mathematics, the rate of change of a function with respect to a variable. Geometrically, the derivative of a function can be interpreted as the slope of the graph of the function or, more precisely, as the slope of the tangent line at a point
What is derivative in math example?
For example: The slope of a constant value (like 3) is always 0. The slope of a line like 2x is 2, or 3x is 3 etc. and so on.



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What is derivative example ?
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======================What are Derivative Instruments? A derivative is an instrument whose value is derived from the value of one or more underlying, which can be commodities, precious metals, currency, bonds, stocks, stocks indices, etc. Four most common examples of derivative instruments are Forwards, Futures, Options and Swaps.

Application of derivative in daily life?
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============================Application of Derivatives in Real Life
To calculate the profit and loss in business using graphs. To check the temperature variation. To determine the speed or distance covered such as miles per hour, kilometre per hour etc. Derivatives are used to derive many equations in Physics.

What is a derivative used for in everyday life?
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=================================== It is an important concept that comes in extremely useful in many applications: in everyday life, the derivative can tell you at which speed you are driving, or help you predict fluctuations on the stock market; in machine learning, derivatives are important for function optimization

How are derivatives used in business?
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============================== About 83% of companies that use derivatives do so to curb the risk of foreign currencies, 76% of firms use derivatives to hedge against changes in interest rates, 56% seek to protect themselves against commodity-price fluctuations, and 34% use derivatives that are based on equity, or stock, markets

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