Answer:
Option 4
Step-by-step explanation:
Term = n/(4^n)
(n+1)th term = (n+1)/[4^(n+1)]
Ratio: (n+1)/[4^(n+1)] ÷ n/(4^n)
= (n+1)/[4^(n+1)] × (4^n)/n
= [(n+1)/n] × (1/4)
For large n, (n+1)/n approaches 1
[(n+1)/n] × (1/4) approaches 1/4 which is less than 1
Since the ratio is less than 1, series converges
Answer:
Step-by-step explanation:
5
Answer:
Is B (-2,-1),(0,0),(2,1)
Step-by-step explanation:
x y
-2 -1
0 0
2 1
I think!!??
Answer:
0
Step-by-step explanation:
∫∫8xydA
converting to polar coordinates, x = rcosθ and y = rsinθ and dA = rdrdθ.
So,
∫∫8xydA = ∫∫8(rcosθ)(rsinθ)rdrdθ = ∫∫8r²(cosθsinθ)rdrdθ = ∫∫8r³(cosθsinθ)drdθ
So we integrate r from 0 to 9 and θ from 0 to 2π.
∫∫8r³(cosθsinθ)drdθ = 8∫[∫r³dr](cosθsinθ)dθ
= 8∫[r⁴/4]₀⁹(cosθsinθ)dθ
= 8∫[9⁴/4 - 0⁴/4](cosθsinθ)dθ
= 8[6561/4]∫(cosθsinθ)dθ
= 13122∫(cosθsinθ)dθ
Since sin2θ = 2sinθcosθ, sinθcosθ = (sin2θ)/2
Substituting this we have
13122∫(cosθsinθ)dθ = 13122∫(1/2)(sin2θ)dθ
= 13122/2[-cos2θ]/2 from 0 to 2π
13122/2[-cos2θ]/2 = 13122/4[-cos2(2π) - cos2(0)]
= -13122/4[cos4π - cos(0)]
= -13122/4[1 - 1]
= -13122/4 × 0
= 0
