(1 point) each of the following statements is an attempt to show that a given series is convergent or divergent using the comparison test (not the limit comparison test.) for each statement, enter c (for "correct") if the argument is valid, or enter i (for "incorrect") if any part of the argument is flawed. (note: if the conclusion is true but the argument that led to it was wrong, you must enter i.)
1. for all n> 2n> 2, ln(n)n> 1nln⁡(n)n> 1n, and the series ∑1n∑1n diverges, so by the comparison test, the series ∑ln(n)n∑ln⁡(n)n diverges.
2. for all n> 1n> 1, n6−n3< 1n2n6−n3< 1n2, and the series ∑1n2∑1n2 converges, so by the comparison test, the series ∑n6−n3∑n6−n3 converges.
3. for all n> 2n> 2, nn3−9< 2n2nn3−9< 2n2, and the series 2∑1n22∑1n2 converges, so by the comparison test, the series ∑nn3−9∑nn3−9 converges.
4. for all n> 2n> 2, ln(n)n2> 1n2ln⁡(n)n2> 1n2, and the series ∑1n2∑1n2 converges, so by the comparison test, the series ∑ln(n)n2∑ln⁡(n)n2 converges.
5. for all n> 1n> 1, 1nln(n)< 2n1nln⁡(n)< 2n, and the series 2∑1n2∑1n diverges, so by the comparison test, the series ∑1nln(n)∑1nln⁡(n) diverges.
6. for all n> 1n> 1, ln(n)n2< 1n1.5ln⁡(n)n2< 1n1.5, and the series ∑1n1.5∑1n1.5 converges, so by the comparison test, the series ∑ln(n)n2∑ln⁡(n)n2 converges.

the answer is the option b

the range is all real numbers

step-by-step explanation:

we know that

the absolute value parent function is equal to

see the attached figure to better understand the problem

so

a. it is v-shaped > is true

b. the range is all real numbers > is not true

because the range is the > [0,∞)

all real numbers greater than or equal to zero

c. it goes through the origin > is true

d. the domain is all real numbers > is true

step-by-step explanation:

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

answer is b

step-by-step explanation:

answer: im sorry i dont get it

step-by-step explanation: