Discuss how you can use the zeros of the numerator and the zeros of the denominator of a rational function to determine whether the graph lies below or above the x-axis in a specified interval?
If the first derivative of a function is greater than 0 on an interval, then the function is increasing on that interval. If the first derivative of a function is less than 0 on an interval, then the function is decreasing on that interval. If the second derivative of a function is greater than 0 on an interval, then the function is concave up on that interval. If the second derivative of a function is less than 0 on an interval, then the function is concave down on that interval.
One.
what exponential function is the average rate of change for the interval from x = 7 to x = 8.
Yes. A well-known example is the function defined as: f(x) = * 1, if x is rational * 0, if x is irrational Since this function has infinitely many discontinuities in any interval (it is discontinuous in any point), it doesn't fulfill the conditions for a Riemann-integrable function. Please note that this function IS Lebesgue-integrable. Its Lebesgue-integral over the interval [0, 1], or in fact over any finite interval, is zero.
What is the area bounded by the graph of the function f(x)=1-e^-x over the interval [-1, 2]?
f(x) is decreasing on the interval on which f'(x) is negative. So we want: (x2-2)/x<0 For this to be true either the numerator or the denominator (but not both) must be negative. On the interval x>0, the numerator is negative for 0<x<sqrt(2) and the denominator is positive for all x>0. On the interval x<0, the denominator is negative for all values on this interval. The numerator is positive on this interval for x<-sqrt(2). So, f' is negative (and f is decreasing) on the intervals: (-infinity, -sqrt(2)), (0, sqrt(2))
It is mathematically impossible to use arc length and an interval alone to determine a function!
If the first derivative of a function is greater than 0 on an interval, then the function is increasing on that interval. If the first derivative of a function is less than 0 on an interval, then the function is decreasing on that interval. If the second derivative of a function is greater than 0 on an interval, then the function is concave up on that interval. If the second derivative of a function is less than 0 on an interval, then the function is concave down on that interval.
A function is positive on an interval, say, the interval from x=a to x=b, if algebraically, all the y-coordinate values are positive on this interval; and graphically, the entire curve or line lies above the x-axis.on this interval.
One.
The question was, let f(x) = 2x if x < -2, ...2x - 2 if -2 <= x <= 2, and ...-2 if x < -2; and what is its graph. You might call this a piecewise-defined linear function. The easiest way to determine this is to look at each interval and see: * Is the function a straight line on each whole interval? * Can you pick two points on each interval so that they match the equation? * And is it a function? Do that and you'll be able to tell. E-mail me if you have more questions on this.
Yes.
Acceleration = (speed at the end of some time interval minus speed at the beginning of the interval)/(length of the time interval)
Yes.
The standard deviation is used in the numerator of the margin of error calculation. As the standard deviation increases, the margin of error increases; therefore the confidence interval width increases. So, the confidence interval gets wider.
2
The contour interval