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Verify means values theorem for the function f(x) = 4x³-4x in the interval [a,b], where a=0, and b=3.
Find a vector of magnitude 6, which is perpendicular to both the vectors and
In a certain isolated population p (t) the rate of population growth is equal to
, where k and ɛ are both positive constants. If p (0) = 1, then find the limiting population as t→ ∞.
An open storage bin with square base and vertical sides is to be constructed from a given amount of material. Determine its dimensions if its volume is to be maximum neglecting the thickness of material and waste in constructing it.
Prove that
Using vectors, find the area of the triangle ABC with vertices A(1,2,3), B(2, -1, 4) and C(4,5,-1).