The ratio of the numerator to the denominator of a fraction is 2 to 3. If both the numerator and the denominator are increased b
2 answers:
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It depends on what you mean by the delimiting carats "^"...
Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for
.
In that case, you want to find the antiderivative,
Complete the square in the denominator:
Now substitute
, so that 
. Then
which simplifies to
Now, recall that
. But we want the substitution we made to be reversible, so that
which implies that
. (This is the range of the inverse sine function.)
Under these conditions, we have
, which lets us reduce 
. Finally,
and back-substituting to get this in terms of
yields
Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for
In that case, you want to find the antiderivative,
Complete the square in the denominator:
Now substitute
which simplifies to
Now, recall that
which implies that
Under these conditions, we have
and back-substituting to get this in terms of
Answer:
A
Step-by-step explanation:
Two facts need to guide your answer.
One
The highest power is odd: you know this because an even power would start on the left come down do it's squiggles if had any and wind up on the right going up.
This graph comes down on the left does it's squiggles and then goes further down on the right. That's the behavior of something whose highest power is odd.
Two
The leading coefficient, the number in front of the highest power must be minus. If it was positive as in y = x^3 the graph would be the mirror image of what it is.
Argument
B and D cannot be true. The highest power is even.
C is false because the leading coefficient is + 1.
So that leave A which is the answer.
The graph is included with this answer
