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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.
From top of a tower a stone is thrown up and it reaches the ground in time t1. A second stone is thrown down with the same speed and it reaches the ground in t2. A third stone is r
the formulas of the area of solid figures
25% of babies born at Yale New Haven Hospital weigh less than 6 pounds and 78% weigh less than 8.5 pounds. What percent of the babies born at Yale New Haven Hospital weigh among 6
Common Graphs : In this section we introduce common graph of many of the basic functions. They all are given below as a form of example Example Graph y = - 2/5 x + 3 .
25 cookies have to be divided equally among 4 children.hw can we use elps to answer this question?
what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n Solution) limit n-->inf. [1 + (n!-n^n)/n^n]^1/n = e^ limit n-->inf. {(n!-n^n)
Q. lim x tends to 0 (5 tanx sinx upon x square) here ( ) this bracket indicates greatest integer function Ans: You can calculate the limit of this function using basic concept of
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A sinking ship signals to the shore for assistance. Three individuals spot the signal from shore. The ?rst individual is directly perpendicular to the sinking ship and 20 meters in
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