The first four terms of the sequence are 3 , 6 , 12 , 24
Step-by-step explanation:
We need to find the first four terms of the sequence 
where 
to find them do that
- Substitute n by 2 in the rule to find
- Substitute n by 3 in the rule to find
- Substitute n by 4 in the rule to find
∵
- Substitute n by 2 to find the 2nd term
∴ 
∴ 
∵
∴ 
∴ 
- Substitute n by 3 to find the 3rd term
∴ 
∴ 
∵
∴ 
∴ 
- Substitute n by 4 to find the 4th term
∴ 
∴ 
∵
∴ 
∴ 
The first four terms of the sequence are 3 , 6 , 12 , 24
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Answer:
a) 28,662 cm² max error
0,0111 relative error
b) 102,692 cm³ max error
0,004 relative error
Step-by-step explanation:
Length of cicumference is: 90 cm
L = 2*π*r
Applying differentiation on both sides f the equation
dL = 2*π* dr ⇒ dr = 0,5 / 2*π
dr = 1/4π
The equation for the volume of the sphere is
V(s) = 4/3*π*r³ and for the surface area is
S(s) = 4*π*r²
Differentiating
a) dS(s) = 4*2*π*r* dr ⇒ where 2*π*r = L = 90
Then
dS(s) = 4*90 (1/4*π)
dS(s) = 28.662 cm² ( Maximum error since dr = (1/4π) is maximum error
For relative error
DS´(s) = (90/π) / 4*π*r²
DS´(s) = 90 / 4*π*(L/2*π)² ⇒ DS(s) = 2 /180
DS´(s) = 0,0111 cm²
b) V(s) = 4/3*π*r³
Differentiating we get:
DV(s) = 4*π*r² dr
Maximum error
DV(s) = 4*π*r² ( 1/ 4*π*) ⇒ DV(s) = (90)² / 8*π²
DV(s) = 102,692 cm³ max error
Relative error
DV´(v) = (90)² / 8*π²/ 4/3*π*r³
DV´(v) = 1/240
DV´(v) = 0,004
