Choose the correct answer.​

1) D: none of them

2) C: ae^(ax)

3) A: cot x

4) A: (3,0)

Step-by-step explanation:

1) the degree of the denominator is more than that of the numerator, thus as n approaches infinity, the function would approach zero. The answer is not available among the options

2) y = e^(ax)

dy/dx = ae^(ax)

3) y = log(sin x)

dy/dx = (1/sin x) × d(sin x)/dx

dy/dx = cosx/sin x

dy/dx = 1/(sin x/cos x)

We know from trigonometry that sin x/cos x = tan x. Thus

dy/dx = 1/tan x

dy/dx = cot x

4) An inflection point is usually the point where the second derivative is equal to zero.

f(x) = x³ - 9x²

f'(x) = 3x² - 18x

f"(x) = 6x - 18

Equating to zero gives;

6x - 18 = 0

x = 18/6

x = 3

Thus the inflection point is (3,0)

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