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The HCF & LCM of two expressions are respectively (x+3) and (x cube-7x+6). If one is x square+2x-3 , other is? Solution) (x+3) * (x^3-7x+6) = (x^2+2x-3) * y ( ) (HCF*LCM=
a) Let n = (abc) 7 . Prove that n ≡ a + b + c (mod 6). b) Use congruences to show that 4|3 2n - 1 for all integers n ≥ 0.
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Magnitude - Vector The magnitude, or length, of the vector v → = (a1, a2, a3) is given by, ||v → || = √(a 1 2 + a 2 2 + a 2 3 ) Example of Magnitude Illus
Example: If c ≠ 0 , evaluate the subsequent integral. Solution Remember that you require converting improper integrals to limits as given, Here, do the integ
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Logarithm Functions : Now let's briefly get the derivatives for logarithms. In this case we will have to start with the following fact regarding functions that are inverses of ea
At times we consider only the magnitude of the number without attaching much importance to its direction. Under these circumstances the sign attached with the num
Q. Show Inverse Trigonometric Functions? Ans. Many functions, including trig functions, are invertible. The inverse of trig functions are called ‘inverse trig functions'.
from 0->1: Int sqrt(1-x^2) Solution) I=∫sqrt(1-x 2 )dx = sqrt(1-x 2 )∫dx - ∫{(-2x)/2sqrt(1-x 2 )}∫dx ---->(INTEGRATION BY PARTS) = x√(1-x 2 ) - ∫-x 2 /√(1-x 2 ) Let
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