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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.
How may six digit numbers can be made in which the sum of the digits is even? Ans = 9*10*10*10*10*5
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A vertical post stands on a horizontal plane. The angle of elevation of the top is 60 o and that of a point x metre be the height of the post, then prove that x = 2 h/3 .
What are some of the interestingmodern developments in cruise control systems that contrast with comparatively basic old systems
From an aero plane vertically above a straight horizontal road, the angles of depression of two consecutive milestones on opposite sides of the aero plane are observed
how are indian customers visiting shoppers stop any different from customers of developed western countries
what is $6500 jamaican dollars in european money if jamaican $160.13 = 1 european money
Q. Definition of Random Variables? Ans. Up to this point, we have been looking at probabilities of different events. Basically, random variables assign numbers to element
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