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Tangent, Normal and Binormal Vectors
In this part we want to look at an application of derivatives for vector functions. In fact, there are a couple of applications, but they all come back to requiring the first one.
In the past we have employed the fact that the derivative of a function was the slope of the tangent line. Along with vector functions we obtain exactly similar result, along with single exception.
There is a vector function, r→ (t) , we call →r′ (t) the tangent vector specified by it exists and provided →r′ (t) ≠ 0 . After that the tangent line to →r (t) at P is the line that passes via the point P and is parallel to the tangent vector, →r′ (t).
Notice: we really do need to require r?′ (t) ≠ 0 to have a tangent vector. Whether we had →r′(t) = 0→ we would have a vector that had no magnitude and thus could not give us the direction of the tangent.
Ratio - situations in which we need to compare two quantities in terms of their ratio. (e.g., if Munna weighs 40 Kg. and Munni weighs 50 Kg., find the ratio of their weights.)
Q. Find a common factor of the numerator and denominator? Ans. There's only one key step to simplifying (or reducing) fractions: find a common factor of the numerator and
1. Consider the trigonometric function f(t) = (a) What is the amplitude of f(t)? (b) What is the period of f(t)? (c) What are the maximum and minimum values attained by
matrix
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Evaluate following limits. Solution : Let's do the first limit & in this case it sees like we will factor a z 3 out of the numerator and denominator both. Remember that
what is the simplest form of 6:9?
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1. Let M be the PDA with states Q = {q0, q1, and q2}, final states F = {q1, q2} and transition function δ(q0, a, λ) = {[q0, A]} δ(q0, λ , λ) = {[q1, λ]} δ(q0, b, A) = {[q2
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