Assume fn → f on a set A. Theorem 6.2.6 is an example of a typical type of question which asks whether a trait possessed by each f, is inherited by the limit function. Provide an example to show that all of the following propositions are false if the convergence is only assumed to be pointwise on A. Then go back and decide which are true under the stronger hypothe sis of uniform conver

(a) If each fn is uniformly continuous, then f is uniformly continuous
(b) If each fn is bounded, then f is bounded.
(c) If each fn has a finite number of discontinuities, then f has a finite number of discontinuities
(d) If each fn has fewer than M discontinuities (where M N is fixed), then f has fewer than M discontinuities.
(e) If each fn has at most a countable number of discontinuities, then f has at most a countable number of discontinuities

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step-by-step explanation:

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the answer is b

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week