MTH631 Quiz by S Khan Academy

SOLVED BY SANAULLAH KHAN · MTH631 QUIZ FILE · Subject Enrolment · 1. Online classes are available (Mathematics) · 2. Solved graded activities · Assignment’s · Quizzes · GDB’s · 3. Solved quiz files · 4. Past papers · 5. Any info about virtual university of · Pakistan · Final project (MTH620) · Email: · Mr.khan.1431 · S KHAN ACADEMY · the term-by-term differentiation of the series is S(x)=

0 ( 1) (2

1)! n

n

n x

n

0 ( 1) (2 )! n

n

n x

n

The linear term of Taylor’ series of f(x)= sin x about

x = is;

If a power series

)n

n

n a x x

converges to a function

f x , then the domain of

f x is ……….as that of the interval of convergence of power series.

Same and equal

The infinite series expansion of cos x for

x

 is given by

( 1) 2 ! n

n

n x

n

Which of the following can never be as the precise set of points of convergence

of a power series ?

Intersection of open interval on Real Line

Let f be defined by a power series with finite radius of convergence R. then

lim n

n n x x R f x a R

only if

n

n n a R

converges

The radius of convergence of the power series

)n

n

n a x x

is

lim n

n n a

R a

If the two power series

n

n

n c x

and

n

n

n d x

defined on the same interval of

convergence say (

r r r  such that, n n

n n

n n c x d x

,then………………where

n  .

Necessarily

n n c d

If (-R,R) the interval of convergence of the power series

n

n

n f x a x

,then the

convergence of power series at x

R =  , depend on the …….

Continuity of

f x

In the definition of uniform convergence, the natural number N always depend

on

(epsilon)

Let f be defined by power series with finite radius of convergence R. then

lim n

n n x x R f x a R

only if

n

n n a R