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Given the properties of the function ( F(x) ), we can start by calculating ( F(1) = 1 ). Using the recursive relation ( F(x+1) = F(x) + 3x(x+1) + 1 ), we can compute the subsequent values:
- ( F(2) = F(1) + 3 \cdot 1 \cdot 2 + 1 = 1 + 6 + 1 = 8 )
- ( F(3) = F(2) + 3 \cdot 2 \cdot 3 + 1 = 8 + 18 + 1 = 27 )
- ( F(4) = F(3) + 3 \cdot 3 \cdot 4 + 1 = 27 + 36 + 1 = 64 )
- ( F(5) = F(4) + 3 \cdot 4 \cdot 5 + 1 = 64 + 60 + 1 = 125 )
- ( F(6) = F(5) + 3 \cdot 5 \cdot 6 + 1 = 125 + 90 + 1 = 216 )
The values are ( F(2) = 8 ), ( F(3) = 27 ), ( F(4) = 64 ), ( F(5) = 125 ), and ( F(6) = 216 ). The function exhibits a polynomial growth pattern, possibly resembling ( F(n) = n^3 ) as the outputs correspond to cubes of natural numbers.
What else can I help you with?
What is the difference between a logarithmic function and a natural exponential function?
The exponential function, in the case of the natural exponential is f(x) = ex, where e is approximately 2.71828. The logarithmic function is the inverse of the exponential function. If we're talking about the natural logarithm (LN), then y = LN(x), is the same as sayinig x = ey.
What does letter E mean in math?
e is Euler's number. It is the base of the natural logarithm and has many interesting and mathematically useful properties. For example, the slope of the function ex is ex, meaning that the slope at any point is equal to the y-value of the function. e is in infinite decimal, the first digits of which are 2.71
What is the difference in the Natural Logarithmic Function and the Common Logarithmic Function?
Natural logarithms use base e (approximately 2.71828), common logarithms use base 10.
What is the difference between a logarithmic function and a natural logarithmic function?
Ans: A natural log function ALWAYS has base e ( e is the irrational number that is the sum of the infinite series 2 + 1 / 2! + 1 /3! + 1 /4! + . . . )
What is natural division?
Natural division refers to a method of dividing a whole into parts based on inherent characteristics or relationships, often seen in biological or ecological contexts. In mathematics, it can also describe a division that reflects the natural structure of numbers, such as when dividing a set into evenly sized groups. This concept emphasizes understanding the intrinsic properties of the entities being divided, rather than an arbitrary or artificial separation.
Who describe the name of electron?
In the Greek language electron is amber, natural mineral with electrical properties, the first discovered.
Who invented physical properties?
Physical properties are inherent characteristics of matter that can be observed or measured without changing the substance's identity. They were not invented by any specific individual; rather, they have always existed as properties of matter in the natural world. Scientists and early philosophers have worked over centuries to understand and describe these properties.
What are the properties of natural rubber?
have elastic properties
What are the properties of a natural lake?
Watery
What are the properties of fiber?
natural fibre ..................
Sampling error concerns natural variation between samples is always present and can be described using probability Is this true?
No, it is not true. Probability can be used to describe some properties of the variation but not all.
How can you classify any properties of matter?
Examples: - solid, liquid or gas - organic or inorganic - colored or colorless - pure or impure - single compound or a mixture - toxic or not - natural or artificial etc.
What are the properties of natural fiber?
Natural fibers are derived from plants, animals, or minerals. They are biodegradable, renewable, and breathable. They can be soft, comfortable to wear, and have good moisture-wicking properties.
What are the two meanings of science?
The root word from the Latin is scienta meaning "to know". So the function of science is to determine the facts regarding a subject.
What term can be used to describe by natural selection?
The term that is often incorrectly used to describe evolution by natural selection is "survival of the fittest."
What term can be used to describe evolution by natural?
The term that is often incorrectly used to describe evolution by natural selection is "survival of the fittest."
What is a synthetic analog?
A synthetic analog is a: synthetically created compound that differs from the Natural compound Both in it's structure and function. Although probably very similar to the original compound.
