a.
To find: The first six polynomials in the given series.
a.
Answer to Problem 47E
The first six polynomials of the series are said to be,
Explanation of Solution
Given information:
The series of polynomials is given as follows.
The
Calculation:
As given in the question, the last term of the fourth polynomial can be calculated as follows.
The last term of the third polynomial is
Then this is added to the third polynomial.
The next two polynomials can be obtained according to the above process.
And
b.
To graph:The first six polynomials in the series given.
b.
Explanation of Solution
Given information:
The series of polynomials has been calculated as follows.
Graph:
The following graph shows all the six polynomials in the series.
Each line in different colors represents a polynomial in the series.
c.
To find:The derivative of the polynomial
c.
Answer to Problem 47E
The derivative of the sixth polynomials of the series isfound to be,
And it is identical to the fifth polynomial.
Explanation of Solution
Given information:
The fifth and sixth polynomial of the seriesaresaid to be,
Calculation:
The derivative of the sixth polynomial can be determined as follows.
As calculated above, the derivative of the sixth polynomial is identical to the fifth polynomial. This can be plotted in the same figure.
Comparing these two functions, a conclusion can be made as these two polynomials closely vary for larger
d.
To find:The function this series of polynomials is approaching.
d.
Answer to Problem 47E
These polynomials approach to the exponential function
Explanation of Solution
The series of polynomial which discussed in this question can be shortened as follows.
Here by factorial
In a long run, when
If a function is said to be an exponential function of
The exponential function is expanded/defined as follows.
Hence, this series of polynomials approaches the exponential function of
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Chapter 2 Solutions
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