For each statement, briefly explain why it is true or false; absent an explanati
ID: 2985827 • Letter: F
Question
For each statement, briefly explain why it is true or false; absent an explanation, even if the true-false answer is correct, zero points will result.
1) Any function can have all of a gap, removable discontinuity, and limit at a given point
2) Vectors r%u2019(t) and r%u2019%u2019(t) always originate at the origin.
3) If, in tranversing an unbanked curve, a car%u2019s speed is doubled, the centripetal force required to avoid skidding is doubled. If, in tranversing an unbanked curve, a car%u2019s speed is doubled, the centripetal force required to avoid skidding is doubled.
4) The result of integrating arc length parameter s from a to b is unknown without a specific example and actual integration.
Explanation / Answer
1) A removable discontinuity at x=a is removed by letting f(a)=lim(f(x)) x->a.
Hence any function with a removable discontinuity has a limit at that point.
2) I can't read the formatting correctly, but most times vectors originate at the origin. However, one is free to move a vector to anywhere in the vector space if not performing a vector operation on it.
3) The centripetal force is proportional to v^2, so false.
4) The result of integration is a number. If you knew the functional form of s, you may be able to write the anti-derivative evaluated from a to b, which is an answer of exactly the length of the parameter on that interval. But without an explicit functional form (or perhaps direct anti-differentiation is not possible), the result is ambiguous.
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