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Problem 1 Let ~x0 = A~x and y 0 = B~y be two 2 2 linear systems of ODE. (1) Suppose that A and B have the same purely imaginary eigenvalues. Prove that these systems are topologi
If cos?+sin? = √2 cos?, prove that cos? - sin? = √2 sin ?. Ans: Cos? + Sin? = √2 Cos? ⇒ ( Cos? + Sin?) 2 = 2Cos 2 ? ⇒ Cos 2 ? + Sin 2 ?+2Cos? Sin? = 2Cos 2 ? ⇒
what are reason inside a circle?
If e were rational, then e = n/m for some positive integers m, n. So then 1/e = m/n. But the series expansion for 1/e is 1/e = 1 - 1/1! + 1/2! - 1/3! + ... Call the first n v
Q. Converting Mixed Numbers to Improper Fractions? Ans. Converting a mixed number to an improper fraction is easy. A single multiplication, and then a single addition:
A circle touches the sides of a quadrilateral ABCD at P, Q, R and S respectively. Show that the angles subtended at the centre by a pair of opposite sides are supplementary.
Graph y = tan ( x ). Solution In the case of tangent we need to be careful while plugging x's in since tangent doesn't present wherever cosine is zero (remember that tan x
3 1/2 x 1 4/7 x 1 1/3
how to get harmonic problems with answer
E1) Create a guessing game for children of Class 2, to familiarise them with the concept of a time interval E2) How could you use group dancing to teach concepts of geometry? Th
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