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Find the smallest positive integer N that satisfies all of the following conditions:
• N is a square.
• N is a cube.
• N is an odd number.
• N is divisible by twelve prime numbers.
How many digits does this number N have?
Find the area of the surface that is generated by revolving the portion of the curve y=x^2 between x=0 and x=1 about the y-axis.
A a parabola having a vertex located at (-4,-8) interpreted the x-axis at x=-2 and x=-6. Determine the length of the arc of this parabola from the interpreted points.
Find the tangent to the parabola y2 = 6x − 3 perpendicular to the line x + 3y = 7
Find the tangent to the parabola y
2 = 6x − 3 perpendicular to the line x + 3y = 7
Find the rate at which the reciprocal of a number changes as the number increases.
Find the volume of the largest rectangular solid which can be inscribed in the
ellipsoid
x
2
a2
+
y
2
b
2
+
z
2
c
2
= 1
Uxx + Uyy =0 convert the situation equation into its Canonical form and find out its general solution
Use the principle of mathematical induction to show that
| sin nx| ≤ n| sin x|
for all n∈ N and for all x ∈ R
Evaluate the line integral
∫𝒖(𝑥, 𝑦, 𝑧) × ⅆ𝒓 ,
where 𝒖(𝑥, 𝑦, 𝑧) = (𝑦^2 , 𝑥, 𝑧) and the curve 𝑪 is described by 𝒛 = 𝑦 = 𝑒 𝑥 with 𝑥 ∈ [0,1].
