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Solve the recurrence relation
T (K) = 2T (K-1), T (0) = 1
Ans: The following equation can be written in the subsequent form:
tn - 2tn-1 = 0
Here now successively replacing n by (n - 1) and then by (n - 2) and so on we obtain a set of equations.
The method is continued till terminating condition. Add these equations in such type of a way that all intermediate terms get cancelled. The equation can be rearranged as
Multiplying all the equations correspondingly by 20, 21, ..., 2n - 1 and then adding them together, we get
tn - 2nt0 = 0
or, tn = 2n
A solution to a differential equation at an interval α Illustration 1: Show that y(x) = x -3/2 is a solution to 4x 2 y′′ + 12xy′ + 3 y = 0 for x > 0. Solution : We'll
Express the GCD of 48 and 18 as a linear combination. (Ans: Not unique) A=bq+r, where o ≤ r 48=18x2+12 18=12x1+6 12=6x2+0 ∴ HCF (18,48) = 6 now 6
(1) Show that the conclusion of Egroff's theorem can fail if the measure of the domain E is not finite. (2) Extend the Lusin's Theorem to the case when the measure of the domain E
Equations of Planes Earlier we saw a couple of equations of planes. Though, none of those equations had three variables in them and were actually extensions of graphs which we
The ratio of the sum of first n terms of two AP's is 7n+1:4n+27. Find the ratio of their 11th terms . Ans: Let a 1 , a 2 ... and d 1 , d 2 be the I terms are Cd's of t
Rajun uses 2/3 of a carton of milk to make a pancake. The volume of milk he uses is 800ml. calculate the volume, in l, of a milk in carton?
2x40 420x4 7x240 84x20 Explain how three expressions are equivalent.
what is the consective sum for 2+3
what is the perimeter of a rhombus
F(x)=2x+3
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