What's 67997 times 8384883
2 answers:
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Combining the terms into one fraction, we have
If this converges to 0 as , then the degree of the numerator must be smaller than the degree of the denominator.
To ensure this, take and
. This eliminates the cubic and quadratic terms in the numerator, and we do have
Alternatively, we can compute the quotient and remainder of the rational expression.
Then in the limit, we have
Both terms on the left vanish if and
.
Answer: The ratios are both identical. (Choice A)
Why does this answer work?
Well let's refer to the diagram below.
Angle x has side 12 opposite it and the hypotenuse is 13.
This means sin(x) = opposite/hypotenuse = 12/13
Also, angle y has side 12 adjacent to it, meaning,
cos(y) = adjacent/hypotenuse = 12/13
Both trig ratios result in 12/13 and we can say sin(x) = cos(y)
One last thing to notice is that x+y = 90
In other words, if x+y = 90, then sin(x) = cos(y)
Phrased a slightly different way: if x+y = 90, then sin(y) = cos(x)
