Evaluate .

Difficulty Rating: 

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Solution: It's easiest to do these problems (as x approaches infinity) when we are dealing with a fraction. So, we transform this into a fraction by multiplying the numerator and denominator by the conjugate and simplify. We then notice that the degree of the numerator is equal to the degree of the denominator (the denominator actually has two x's to the first power), so we take the coefficients of the x's, perform the addition in the denominator, and are finished:

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Calculus II (BC): Vectors

Given  and , find and justify your answers to the following:

Difficulty Rating: 

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Solution: Once vectors are in component, or <x, y>, form, it's easy to find the norm, or length of them with the Pythoagorean Theorem, as it is assumed the initial point of the vector is the origin. Parts (d), (e), and (f) are extremely simple, as they are merely the very formulas for normalizing vectors (creating a unit vector in the same direction as the given vector).

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