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1. I Order of derivatives

If v is of order δ, what is the order of ∂v/∂x and ∂2v/∂x2 ?
2. Tangent vector

But the rate of change at a point can never be a tangent at that point. It has to be integrated to obtain the equation of the tangent.
3. Tangent vector

Then why is the rate of change called the tangent vector itself?
4. Tangent vector

I was reading about the tangent vector at a point on a curve. It is formulated as r' = Lim Δt→0 [r(t+Δt) - r(t)] / Δt (sorry for the misrepresentation of the 'Lim Δt→0 ') where r(t) is a position vector to the curve and t is a parameter and r' is the derivative of r(t). All I can...
5. What is an integrating factor exactly?

I'm sorry about the question not matching the title. I didn't realize when posting it. Your guess sounds right. Thanks.
6. What is an integrating factor exactly?

While solving non-homogenous linear ODEs we make use of the integrating factor to allow us to arrive at a solution of the unknown function. Same applies to non linear ODEs where the ODEs are converted to exact differentials. But what I don't understand is how and why would someone have come up...
7. Concept of limit

Well, I actually had a fundamental doubt (silly even) for which reason I had posted the question mainly. I am a newbie to the concept of limits. My doubt is as follows. Why should we look to modify the numerator or the denominator or both? Why not just consider that as n tends to infinity the...
8. Concept of limit

How can it be proved that as lim n tends to infinity, (n2-1)/(n2 + n + 1) tends to 1 ?
9. Why are transcendental functions called so?

I see. Thank you pwsnafu.
10. Why are transcendental functions called so?

I have learnt that they are called so because they cannot be expressed with the help of elemental methods of mathematics such as addition, subtraction, multiplication and division. But then isn't the whole of mathematics itself based on the elemental methods?