Question

(a) (1 point) If at converges conditionally, then lak| diverges. Answer: True / False (b) (1 point) Suppose that a power series Eck(-a)* converges for - al > R and defines a function f on that interval. The differentiated or integrated power series converge, provided x belongs to the interior of the interval of convergence. It also claim about the convergence of the differentiated or integrated power series at the endpoints of the interval of convergence. Answer: True / False (c) (1 point) Taylor series centered at 0 is called a Maclaurin series. Answer: True / False d) (1 point) The parametric description of a given line is unique. Answer: True / False

Answer 1

1. True

Conditional Convergence
A series summation(ak) is said to converge conditionally ifsummation (ak) converges while summation |ak| diverges.

2. False

4.5.1. Convergence of Power Series. For a given power series summantion cn(x − a)^n
n there are only three possibilities:
(1) The series converges only for x = a.
(2) The series converges for all x.
(3) There is a number R, called radius of convergence, such that
the series converges if |x − a| < R and diverges if |x − a| > R.
The interval of convergence is the set of values of x for which the series converges.

3.True

The Taylor Series for f(x) centered at x = c is. If c = 0, then the series is calledthe Maclaurin series for f

4.False

Parametric representations are generally nonunique .so the same quantities may be expressed by a number of different parameterizations.

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