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Extreme Value Theorem : Assume that f ( x ) is continuous on the interval [a,b] then there are two numbers a ≤ c, d ≤ b so that f (c ) is an absolute maximum for the function and
There is a list of the forces which will act on the object. Gravity, F g The force because of gravity will always act on the object of course. Such force is F g = mg
A golf ball has a diameter equal to 4.1cm. Its surface has 150 dimples each of radius 2mm. Calculate the total surface area which is exposed to the surroundings assuming that the d
Theorem, from Definition of Derivative If f(x) is differentiable at x = a then f(x) is continuous at x =a. Proof : Since f(x) is differentiable at x = a we know, f'(a
Steps for Alternating Series Test Suppose that we have a series ∑a n and either a n = (-1) n b n or a n = (-1) n+1 b n where b n > 0 for all n. Then if, 1.
A lotus is 2m above the water in a pond. Due to wind the lotus slides on the side and only the stem completely submerges in the water at a distance of 10m from the original positio
On 30 June 2012 Bill purchase a home by taking out a 30 year mortgage of $600,000 at 6% interest per annum, compounded months. Repayments are made at the end of each month. (a) Cal
un=63-4n
We know that a factor is a quantity which divides the given quantity without leaving any remainder. Similar to LCM above we can find a highest common factor (HCF)
a rectangular field with a path around it measures 120m by 50m.if the path is 1m wide all around,(a)find the length of the outer edge of the path.(b)find the area of the path
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