Determine whether the sequence converges or diverges. If it converges, find the limit (if an answer does not exist, enter DNE.) {lnn/ln3}
limn→[infinity]{lnn/ln3n}=

The sequence converges. The limit DNE.

Step-by-step explanation:

Find the limit of n as n tends to infinity (in other words, positive infinity) in {Ln(n)/ Ln(3n)}

Positive infinity values for n start from 1,2,3,4,5,6,7,8,9,10,11,12,13,14,...,infinity

So I solved for values of n, up to n=20. All values are rounded up to 3 decimal places; for better accuracy.

When n is 1, the function is equal to 0.000

When n is 2, the function is = 0.387

When n is 3, the function = 0.500

When n is 4, the function = 0.558

When n is 5, the function = 0.594

When n is 6, the function = 0.619

When n is 7, the function = 0.639

When n is 8, the function = 0.654

When n is 9, the function = 0.667

When n is 10, the function = 0.677

When n is 11, the function = 0.686

When n is 12, the function = 0.693

When n is 13, the function = 0.700

When n is 14, the function = 0.706

When n is 15, the function = 0.711

When n is 16, the function = 0.716

When n is 17, the function = 0.721

When n is 18, the function = 0.725

When n is 19, the function = 0.728

When n is 20, the function = 0.732

We say there is a convergence because the space between the values of n gets smaller and smaller as n tends to infinity and there is no definite limit. Limit DNE.

a) false; the points do not have to be in a straight line.

step-by-step explanation:

the points could be in the shape of a triangle

b is incorrect

c is incorrect because it is saying the immediately don't form one when they are capable of doing so

d is incorrect

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!