The function, named H(w) is defined by a graph that is a descendant line, that belongs only to the first quadrant. As w approaches to 0 by the right, the function approaches to + infinity. It never touches the vetical axis, decreases and approaches to 0 when w approaches to infinity. The graph never touches the horizontal - axis.
Then, the function is defined only for positive values of w and H(w) is always positive.
Then, the answer is H(w) > 0, this is the option C.
How will I answer that, the image isn't showing luv
The roots of the polynomial <span><span>x^3 </span>− 2<span>x^2 </span>− 4x + 2</span> are:
<span><span>x1 </span>= 0.42801</span>
<span><span>x2 </span>= −1.51414</span>
<span><span>x3 </span>= 3.08613</span>
x1 and x2 are in the desired interval [-2, 2]
f'(x) = 3x^2 - 4x - 4
so we have:
3x^2 - 4x - 4 = 0
<span>x = ( 4 +- </span><span>√(16 + 48) </span>)/6
x_1 = -4/6 = -0.66
x_ 2 = 2
According to Rolle's theorem, we have one point in between:
x1 = 0.42801 and x2 = −1.51414
where f'(x) = 0, and that is <span>x_1 = -0.66</span>
so we see that Rolle's theorem holds in our function.
8: 20
9: 90
I am so sorry if this is wrong. I am not good at this type of things
The common difference is 1 1/3
40-1 1/3= 38 2/3
38 2/3-1 1/3=37 1/3
37 1/3-1 1/3=36
Therefore the missing number is 38 2/3
