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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 revolution is. To get a solid of revolution we begin with a function, y = f (x ) , on an interval [a,b].
Then we rotate this curve around a given axis to get the surface of the solid of revolution. For discussion let's rotate the curve around the x-axis, although it could be any vertical or horizontal axis. Carrying out this for the curve above gives the given three dimensional region.
Exponential and Geometric Model Exponential model y = ab x Take log of both sides log y = log a + log b x log y = log a + xlog b Assume log y = Y and log a
round to the nearest hundreths 1677.76
(x^3-9/5x^2+8/5x-4)
find the radius of circumcircle of an equilateral triangle of 6root3 one side.
WHAT IS PLACE VALUE? : (This section is only for your assumptions, and not-meant to be passed on to your learners.) You may have realised that in the decimal system the numeral
Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians of the triangle. Ans: To prove 3(AB 2
remainder theorem
Chain Rule : If f(x) and g(x) are both differentiable functions and we describe F(x) = (f. g)(x) so the derivative of F(x) is F′(x) = f ′(g(x)) g′(x). Proof We will s
Trig function
In order to compute the inequalities of the form where n 1 , n 2 , ....... , n k , m 1 , m 2 , ....... , m p are natural and real numbers and a 1 , a 2 , ... , a k ,
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