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If y 1 (t) and y 2 (t) are two solutions to y′′ + p (t ) y′ + q (t ) y = 0 So the Wronskian of the two solutions is, W(y 1 ,y 2 )(t) = =
Utilizes the definition of the limit to prove the given limit. Solution Let M > 0 be any number and we'll have to choose a δ > 0 so that, 1/ x 2 > M
Confidence Interval The interval estimate or a 'confidence interval' consists of a range as an upper confidence limit and lower confidence limit whether we are confident that a
Infinite Interval - Improper Integrals In this type of integral one or both of the limits that is upper limit and lower limit of integration are infinity. In these cases the
We're here going to take a brief detour and notice solutions to non-constant coefficient, second order differential equations of the form. p (t) y′′ + q (t ) y′ + r (t ) y = 0
If a, b and c are in harmonic progression with b as their harmonic mean then, b = This is obtained as follows. Since a, b and c are in
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 value of x if 2x + 1, x 2 + x +1, 3 x 2 - 3 x +3 are consecutive terms of an AP. Ans: a 2 -a 1 = a 3 -a 2 ⇒ x 2 + x + 1-2 x - 1 = 3x 2 - 3x + 3- x
In this case, the first point we have to remember is that we do not get a single value when we add two or more terms which are unlike in nature. This certainly ob
Can two lines contain a given point
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