I need help on this true or false question for all parts. Thank you A.) Every polynomial with real coefficients can be factored into a product of linear factors with real coefficientsand/or irreducible quadratic factors with real coefficients.B.) If a, >0 and lim a, <1, then lim a, = 0.n00C.) If la, is convergent, thenEa, is also convergent.i=1i=1D.) A polar function can always be written as a parametrically defined function.E.) Suppose a curve C is described by the vector function r(t)= (x(t), y(t),z(t)) where r'(t) is continuousand C is traversed exactly once as t goes from a to b, then the length of C is r(t) dt .F.) If lim a, = 0, then > a, convergesi=1G.) If a power series f (x)=Ea,x* has an interval of convergence I =(-b,b), then | f (x)dx has a powerk=1series with the same interval of convergence.H.) Given a, b and c are nonzero vectors in R', then (axb)•(axc)=0I.) (u+v)•(u- v)=||u|| -||v|| for u and v vectors in R'J) (uxv).w =u•(vxw) for u, v and w vectors in R'.

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Description: I need help on this true or false question for all parts. Thank you A.) Every polynomial with real coefficients can be factored into a product of linear factors with real coefficientsand/or irreducible quadratic factors with real coefficients.B.) If

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A.) Every polynomial with real coefficients can be factored into a product of linear factors with real coefficients and/or irreducible quadratic factors with real coefficients. B.) If a, >0 and lim a, <1, then lim a, = 0. C.) If Ela| is convergent, then a, is also convergent. i=1 i=1

A.) Every polynomial with real coefficients can be factored into a product of linear factors with real coefficients and/or irreducible quadratic factors with real coefficients. B.) If a, >0 and lim a, <1, then lim a, = 0. C.) If Ela| is convergent, then a, is also convergent. i=1 i=1

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

I need help on this true or false question for all parts. Thank you

A.) Every polynomial with real coefficients can be factored into a product of linear factors with real coefficients
and/or irreducible quadratic factors with real coefficients.
B.) If a, >0 and lim a, <1, then lim a, = 0.
n00
C.) If la, is convergent, thenEa, is also convergent.
i=1
i=1
D.) A polar function can always be written as a parametrically defined function.
E.) Suppose a curve C is described by the vector function r(t)= (x(t), y(t),z(t)) where r'(t) is continuous
and C is traversed exactly once as t goes from a to b, then the length of C is r(t) dt .
F.) If lim a, = 0, then > a, converges
i=1
G.) If a power series f (x)=Ea,x* has an interval of convergence I =(-b,b), then | f (x)dx has a power
k=1
series with the same interval of convergence.
H.) Given a, b and c are nonzero vectors in R', then (axb)•(axc)=0
I.) (u+v)•(u- v)=||u|| -||v|| for u and v vectors in R'
J) (uxv).w =u•(vxw) for u, v and w vectors in R'.

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