EXAMPLE 2 For what values of p is the series [infinity] 1 np n = 1 convergent? SOLUTION If p < 0, then lim n → [infinity] (1/np) = [infinity]. If p = 0, then lim n → [infinity] (1/np) = . In either case, lim n → [infinity] (1/np) ≠ 0, so the given series diverges by the Test for Divergence. If p > 0, then the function f(x) = 1/xp is clearly continuous, positive, and decreasing on [1, [infinity]). Previously, we found that [infinity] 1 xp dx 1 converges if p > and diverges if p ≤ . It follows from the Integral Test that the series Σ 1/np converges if p > and diverges if 0 < p ≤ . (For p = 1, the series is the harmonic series discussed in this example.)

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol

step-by-step explanation:

duck you

80° is the measure of gh

step-by-step explanation:

circle f is congruent to circle j

we have two circle with center f and j.

both circles are congruent. the radius of the circle would be equal.

see the attachment for the circle.

we are given ∠efd ≅ ∠gjh

therefore, arc (ed) = arc (gh)     (∴ circle f is congruent to circle j)

but ∠dfe=80°=arc (ed)

therefore, arc (gh) = 80°

thus, 80° is the measure of gh