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writing sin 3 a.cos 3 a = sin 3 a.cos 2 a.cosa = sin 3 a.(1-sin 2 a).cosa put sin a as then cos a da = dt integral(t 3 (1-t 2 ).dt = integral of t 3 - t 5 dt = t 4 /4-t 6 /6
The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to
From a point P, two tangents PA are drawn to a circle with center O.If OP=diameter of the circle show that triangle APB is equilateral. Ans: PA=PB (length of tangents
Two angles are supplementary. The evaluate of one is 30 more than twice the measure of the other. Determine the measure of the larger angle. a. 130° b. 20° c. 50° d. 70
Determine if the following sequences are monotonic and/or bounded. (a) {-n 2 } ∞ n=0 (b) {( -1) n+1 } ∞ n=1 (c) {2/n 2 } ∞ n=5 Solution {-n 2 } ∞ n=0
Tangent, Normal and Binormal Vectors In this part we want to look at an application of derivatives for vector functions. In fact, there are a couple of applications, but they
3x+2y=6 x-y=7
Exponential and Logarithm Equations : In this section we'll learn solving equations along with exponential functions or logarithms in them. We'll begin with equations which invol
Binomials, Trinomials and Polynomials which we have seen above are not the only type. We can have them in a single variable say 'x' and of the form x 2 + 4
advanteges of duality
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