They will need 3 cars, but one of the cars will be having 3 passengers instead of 4. :)
1.) D = 2pi * d * A / 360 degrees; Where:
pi = 3.14;
d = distance or 56,000,000 km (5.6x10^7 to standard notation)
A = angular size in degrees or .00688 degrees (.00012 radian to degrees)
D = 2(3.14) * 56,000,000 * .00688 / 360
= 6.28 * 385,280 / 360
= 2,419,558.4 / 360
D = 6,720.996 or 6,721
Therefore, 6,721 km. is the approximate diameter of Mars.
Lim[x.sin(4π/x)] when x →∞. To apply the Hospital rule we need a fraction:
lim[x.sin(4π/x)] could be written:
lim [sin(4π/x)] / (1/x) . Now let's find the derivative of the numerator and the denominator:
Numerator = sin(4π/x) → (Numerator)' = cos(4π/x).(-4π/x²) [Chaine rule
(sinu)' = cosu. u'] So derivative of Numerator = cos(4π/x).(-4π/x²)
Denominator = 1/x → Numerator derivative = -1/x²
Now : (numerator)'/(denominator)' = cos(4π/x).(-4π/x²) / -1/x²
Simplify by x² : → cos(4π/x).(-4π) / -1
OR cos(4π/x).(4π) . When x→∞ , 4π/x → 0 and cos(0) = 1, then:
lim[x.sin(4π/x)] when x →∞. is 4π
