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)