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Write following in terms of simpler logarithms. (a) log 3 (9 x 4 / √y) Solution log 3 (9 x 4 / √y) =log 3 9x 4 - log y (1/2) =log 3 9 + log 3 x 4
Find out if the following sets of functions are linearly dependent or independent. (a) f ( x ) = 9 cos ( 2 x ) g ( x ) = 2 cos2 ( x ) - 2 sin 2 ( x ) (b) f
sin30
Draw the direction field for the subsequent differential equation. Draw the set of integral curves for this differential equation. Solution: y′ = y - x To draw direct
Evaluate following indefinite integrals. (a) ∫ 5t 3 -10t -6 + 4 dt (b) ∫ dy Solution (a) ∫ 5t 3 -10t -6 + 4 dt There's not whole lot to do here other than u
Suppose m be a positive integer, then the two integer a and b called congurent modulo m ' if a - b is divisible by m i.e. a - b = m where is an positive integer. The congru
one half y minus 14
Write the next two terms √12, √27, √48, √75................... Ans: next two terms √108 , √147 AP is 2 √3 , 3 √3 , 4 √3 , 5 √3 , 6 √3 , 7 √3 ......
Find the amount of sheet metal need to form a conical funnel of base radius 30cm with a vertical height of 50cm, allowing for 0.5cm overlap. Find the total surface area?
Prove that the Digraph of a partial order has no cycle of length greater than 1. Assume that there exists a cycle of length n ≥ 2 in the digraph of a partial order ≤ on a set A
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