Establish which of the following statements are true. (a) A sequence is convergent if and only if all of its subsequences are convergent. (b) A sequence is bounded if and only if all of its subsequences are bounded. (c) A sequence is monotonic if and only if all of its subsequences are monotonic. (d) A sequence is divergent if and only if all of its subsequences are divergent.

Statement A - True.

Statement B - False.

Statement C - True.

Statement D - False.

Step-by-step explanation:

(a) A sequence is convergent if and only if all of its subsequences are convergent - this statement is correct.

(b) A sequence is bounded if and only if all of its subsequences are bounded - this statement is incorrect.

(c) A sequence is monotonic if and only if all of its subsequences are monotonic - this statement is correct.

(d) A sequence is divergent if and only if all of its subsequences are divergent - this statement is incorrect.

1. a^4+8a^3+24a^2+32a+16

2.y^8+8y^7+28y^6+56y^5+70y^4+56y^3+28y^2+8y+1

3.x^6-3x^4y^2+3x^2y^4-y^6

answer: c

substitute in the values.

for a:

f(0) = 0 + 9

f(0) = 9

a is a solution.

for b:

f(7) = 14 + 9

f(7) = 23

b is a solution.

for c:

f (3) = 6 + 9

f(3) = 15

c is not a solution. it's supposed to be 14.

for d:

f(2) = 4 + 9

f(2)= 13

d is a solution.