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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.
Two circles touch internally at a point P and from a point T on the common tangent at P, tangent segments TQ and TR are drawn to the two circles. Prove that TQ = TR. Given:
If two vertices of an equilateral triangle are (0, 0) and (3, 0), find the third vertex. [Ans: 3/2 , 3/√ 3/2 or 3/2, -3√ 3/2] Ans: OA = OB = AB OA 2 = OB 2 = AB 2
3x+5y
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number of ways that a mixed doubles tennis game can be arranged from 7 couples if no husband and wife play in the same game is??
Sam''s sport''s equipment sells footballs. They maximized their profitability last year at (6,4) where x represents employees and P(x) represents profitability. Sam noticed that wh
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to difine trigonometric ratios of an angle,is it necessary that the initial ray of the angle must be positive x-axis?
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