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An infinite sum of continuous functions does not have to be continuous. For example, you should be able to construct a Fourier series that converges to a discontinuous function.
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What is the sum of all natural numbers?
The sum is infinite
Does the cosine function appear to be continuous?
yes it is a continuous function.
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 does continuous variable mean in science?
A quantitative variable where there is a continuous (no infinite number) of attributes. For example length/height/weight can be measure as continuous as it has not set number
What is the sin function?
It is a trigonometric function. It is also continuous.
Does a sum of infinite ones equal a sum of infinite twos?
Yes, the sum of infinite ones equal the sum of infinite twos.
Is a cosine function continuous?
Yes. The cosine function is continuous. The sine function is also continuous. The tangent function, however, is not continuous.
What is the sum of all natural numbers?
The sum is infinite
Does the cosine function appear to be continuous?
yes it is a continuous function.
A polynomial function is always continuous?
Yes, a polynomial function is always continuous
Every continuous function is integrible but converse is not true every integrable function is not continuous?
That's true. If a function is continuous, it's (Riemman) integrable, but the converse is not true.
What is the fourier series?
It's an infinite sum of sines and cosines that can be used to represent any analytic (well-behaved, like without kinks in it) function.
What function is continuous everywhere but not differentiable?
Weistrass function is continuous everywhere but not differentiable everywhere
Can a function have a limit at every x-value in its domain?
Yes, that happens with any continuous function. The limit is equal to the function value in this case.Yes, that happens with any continuous function. The limit is equal to the function value in this case.Yes, that happens with any continuous function. The limit is equal to the function value in this case.Yes, that happens with any continuous function. The limit is equal to the function value in this case.
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! + . . . )
How many pairs of whole numbers have a sum of 40?
An infinite number.
Is driving speed a discrete or continuous variable?
Speed is a continuous variable since it can take on an infinite set of values.
