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Proof of: if f(x) > g(x) for a x b then a ∫ b f(x) dx > g(x). Because we get f(x) ≥ g(x) then we knows that f(x) - g(x) ≥ 0 on a ≤ x ≤ b and therefore by Prop
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Find out the x-y coordinates of the points in which the following parametric equations will have horizontal or vertical tangents. x = t 3 - 3t y = 3t 2 - 9 Solut
What is the slope and y intercept for (6,5) (-3,8)
Two circles touch internally at a point P and from a point T on the common tangent at P, tangent segments TQ and TR are drawn to the two circles. Prove that TQ = TR. Given:
A die is rolled twice and the sum of the numbers appearing on them is observed to be 7.What is the conditional probability that the number 2 has appeared at least once? A) 1/3
Evaluate following. ∫ 0 ln (1 + π ) e x cos(1-e x )dx Solution The limits are little unusual in this case, however that will happen sometimes therefore don't get
Volumes of Solids of Revolution / Method of Rings In this section we will begin looking at the volume of solid of revolution. We have to first describe just what a solid of rev
If A, B and P are the points (-4, 3), (0, -2) and (α,β) respectively and P is equidistant from A and B, show that 8α - 10β + 21= 0. Ans : AP = PB ⇒ AP 2 = PB 2 (∝ + 4) 2
What kinds of classroom activities can you think of for helping children to make groups of 5 and 10? Once they have enough practice with such activities, children can be helped
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