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Rolle's Theorem
Assume f(x) is a function which satisfies all of the following.
1. f(x) is continuous in the closed interval [a,b].
2. f(x) is differentiable in the open interval (a,b).
3. f(a) = f(b)
So, there is a number c as a < c < b and f′(c) = 0. Or, though f(x) has a critical point in (a,b).
2.When investigating times required for drive-through service, the following results (in seconds) were obtained. Find the range, variance, and standard deviation for each of the tw
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The numbers used to measure quantities such as length, area, volume, body temperature, GNP, growth rate etc. are called real numbers. Another definition of real numbers us
In the adjoining figure, ABCD is a square of side 6cm. Find the area of the shaded region. Ans: From P draw PQ ⊥ AB AQ = QB = 3cm (Ans: 34.428 sq cm) Join PB
Fermat Catalan Conjecture
If the points (5, 4) and (x, y) are equidistant from the point (4, 5), prove that x 2 + y 2 - 8x - 10y +39 = 0. Ans : AP = PB AP 2 = PB 2 (5 - 4) 2 + (4 - 5) 2 = (x
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Write Prim's Algorithm. Ans: Prim's algorithm to find out a minimum spanning tree from a weighted graph in step by step form is given below. Let G = (V, E) be graph and S
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