What is a linear equation that intersects y = x2 at TWO points?
1 answer:
<h3>Answer:</h3>
- y = x intersects at 2 points
- y = -2x-1 intersects at 1 point
- y = x-2 intersects at 0 points
Any line with a y-intercept greater than 0 will intersect y = x² at two points, as will any line with a non-zero slope and a y-intercept of zero. I have chosen the line y = x to answer this question.
Any tangent line will intersect y = x² at one point. A tangent line will have slope 2x at the point (x, x²). Here, we have chosen to write the equation for the tangent at (x, y) = (-1, 1). That line has equation y = -2x-1.
Any line with a negative y-intercept and a sufficiently small slope will not intersect the curve y = x². (The slope needs to have a magnitude less than double the magnitude of the y-intercept.) Here, we have chosen a line with slope 1 and y-intercept -2: y = x-2.
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Answer:
Step-by-step explanation:
a)
Substitute limits to get
=
Thus converges.
b) 10th partial sum =
=
c) Z [infinity] n+1 1 /x ^4 dx ≤ s − sn ≤ Z [infinity] n 1 /x^ 4 dx, (1)
where s is the sum of P[infinity] n=1 1/n4 and sn is the nth partial sum of P[infinity] n=1 1/n4 .
(question is not clear)