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Smooth Curve - Three Dimensional Space
A smooth curve is a curve for which →r' (t) is continuous and →r' (t) ≠ 0 for any t except probably at the endpoints. A helix is a smooth curve, for instance.
At last, there is requirement of discuss integrals of vector functions. By using both limits and derivatives like a guide it shouldn't be too surprising that we as well comprise the following for integration for indefinite integrals
∫ r→ (t) = {∫ f (t)dt, ∫g (t)dt, ∫ h(t) dt} + c→
∫ r→ (t) = ∫ f (t)dt i→ + ∫g (t)dt j→ + ∫ h(t) dt} k→ + c→
and the following for definite integrals.
∫ba r→ (t) dt = {∫ba f (t) dt, ∫ba g (t) dt, ∫ba h(t) dt}
∫ba r→ (t) dt = ∫ba f (t) dt i→ + ∫ba g (t) dt j→ + ∫ba h(t) dt k→
Along with the indefinite integrals we put in a constant of integration to ensure that it was clear that the constant in this case requires being a vector in place of a regular constant.
Sketch the direction field for the subsequent differential equation. Draw the set of integral curves for this differential equation. Find out how the solutions behave as t → ∞ and
The area enclosed between two concentric circles is 770cm 2 . If the radius of the outer circle is 21cm, find the radius of the inner circle. (Ans :14cm) Ans: Π R 2 - Π r 2 =
(a) The generating function G(z) for a sequence g n is given by G(z) = 1 - 2z/(1 + 3z)3 Give an explicit formula for g n . (b) For the sequence gn in the previous part co
In the adjoining figure a dart is thrown at the dart board and lands in the interior of the circle. What is the probability that the dart will land in the shaded region. A
who discovered unitary method
Question: The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature. (a) Construct a decision tr
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The ratio of gasoline to oil needed to run a chain-saw is 16:1. If you have 3.5 mL of oil, how many millilitres of gasoline must you add to get the proper mixture?
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Describe Adding and Subtracting Square Roots? To add or subtract square roots, the radicands must be the same. If the radicands are the same, add/subtract the coefficients (the
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