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Consider the differential equation give by y′ = -10(y - sin t) (a) Derive by hand exact solution that satis?es the initial condition y(0) = 1. (b) Numerically obtain the s
1. A direction ?eld for a differential equation is shown. Draw, with a ruler, the graphs of the Euler approximations to the solution curve that passes through the origin. Use step
Childrens errors are a natural and inevitable part of their process of learning. In the process of grasping new concepts, children apply their existing understanding, which may
The Shape of a Graph, Part I : In the earlier section we saw how to employ the derivative to finds out the absolute minimum & maximum values of a function. Though, there is many
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 ? ⇒
Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a foot ball match? Ans: equally likely because they are mutual
All the number sets we have seen above put together comprise the real numbers. Real numbers are also inadequate in the sense that it does not include a quantity which i
.755 convert to a percent
A department store faces a decision for a seasonal product for which demand can be high, medium or low. The purchaser can order 1, 2 or 3 lots of this product before the season beg
If A, B and P are the points (-4, 3), (0, -2) and (α,β) respectively and P is equidistant from A and B, show that 8α - 10β + 21= 0. Ans : AP = PB ⇒ AP 2 = PB 2 (∝ + 4) 2
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