2. I Using the example { 2/3+4/3 X, explain why we add fractions the way we do. What is the logic behind the procedure? Make mat
1 answer:
Answer:
The procedure emphasizes the idea of the summation of one physical quantity. In this case, X.
Step-by-step explanation:
1. When we add fractions like these we do it simply by rewriting a new one, the summation of the numerators over the same denominator:
The procedure emphasizes the idea of the summation of one physical quantity, in this case, X.
2) This physical quantity x could be miles, oranges, gallons, etc.
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Carry out the binomial expansion in the numerator:
Then the 9⁴ terms cancel each other, so in the limit we have
Since <em>h</em> is approaching 0, that means <em>h</em> ≠ 0, so we can cancel the common factor of <em>h</em> in both numerator and denominator:
Then when <em>h</em> converges to 0, each remaining term containing <em>h</em> goes to 0, leaving you with
or choice C.
Alternatively, you can recognize the given limit as the derivative of <em>f(x)</em> at <em>x</em> = 9:
We have <em>f(x)</em> = <em>x</em> ⁴, so <em>f '(x)</em> = 4<em>x</em> ³, and evaluating this at <em>x</em> = 9 gives the same result, 2916.