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writing sin3a.cos3a = sin3a.cos2a.cosa= sin3a.(1-sin2a).cosaput sin a as then cos a da = dt integral(t3(1-t2).dt= integral of t3- t5 dt= t4/4-t6/6 + c where t = sina
Definition 1. Given any x 1 & x 2 from an interval I with x 1 2 if f ( x 1 ) 2 ) then f ( x ) is increasing on I. 2. Given any x 1 & x 2 from an interval
Basic indefinite integrals The first integral which we'll look at is the integral of a power of x. ∫x n dx = (x n +1 / n + 1)+ c, n
Two circles touching internally at O. OXY, OAB straight lines, the latter passing through the centres. Prove that OX : OY = OA : OB. Given : Two circles touching internally a
If an instrument has precision of +-1, can it detect a value of 1.3?
simplify the expression 3/5/64
Determine if the following series converges or diverges by using limit comparison test. Solution To make use of the limit comparison test we require to find out a seco
AskIf y=e^(a?sin?^(-1) x), prove that (1 – x2)yn+2 – (2n + 1)xyn+1 – (n2 + a2)yn = 0. Hence find the value of yn when x = 0. question #Minimum 100 words accepted#
Vector Arithmetic In this part we need to have a brief discussion of vector arithmetic. Addition We will begin with addition of two vectors. Thus, given the vectors a
Differentiate following functions. (a) R ( w) = 4 w - 5 log 9 w (b) f ( x ) = 3e x + 10x 3 ln x Solution : (a) It will be the only example which doesn't includ
The sum of three consecutive even integers is 102. What is the value of the largest consecutive integer? Three consecutive even integers are numbers in order such as 4, 6, and
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