Answer true or false for each statment. If false, explain why the statment is no

Question

Answer true or false for each statment. If false, explain why the statment is not true or correct the statment.

a. Taylor polynomials are nothing but truncated Taylor series.

b. Taylor series represent infinitely continuous functions over an interval.

c. A Taylor series has a radius of convergence.

d. The degree of an ODE is the highest power to which the highest derivative is raised.

e. The error in a Taylor polynomial representation has at least three analytical representations.

f. The error in a Taylor polynomial representation generally depends on an an unknown constant.

g. The first two terms for the Taylor series of sin(x) are x and (x^3)/6.

h. Since sin(x) is a Taylor polynomial of infinite degree, it still is a polynomial.

i. Taylor series can be used to solve some ODEs.

j. Two Taylor series when divided do not give another Taylor series.

Explanation / Answer

A) Taylor polynomials are nothing but truncated Taylor series.this sentence is true

B)Taylor polynomials are nothing but truncated Taylor series. this sentence is also is true

C)A Taylor series has a radius of convergence. it is also true taylor series has a radius of convergence

D)The degree of an ODE is the highest power to which the highest derivative is raised it is also true the highest derivative is depending upon the highest power of the ODE

e) The error in a Taylor polynomial representation has at least three analytical representations. he error in a Taylor polynomial representation has atleast three analytical epresentation in fact ,there are smoothfinction which are not analytic

F)T he error in a Taylor polynomial representation generally depends on an an unknown constant.It is also true

G) The first two terms for the Taylor series of sin(x) are x and (x^3)/6. this is flase because the first two terms are x-x^3/6

h)Since sin(x) is a Taylor polynomial of infinite degree, it still is a polynomial. it is also true because polynomial means an equation is having the power more than 1

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