g(t)=2+cos t; [0,pi]
Can you help me find the average rate of change of the function over the given interval?
There is no rate of change of the number 2
Graph cos t from 0 to pi
1 at t = 0
0 at t = pi/2
-1 at t = pi
so it drops
now the average rate of change is the function at pi - the function at t all divided by the time, pi
function at pi = -1
function at 0 = +1
(-1 - 1 )/pi = -2/pi
Of course, I'd be glad to assist you with that! To find the average rate of change of the function g(t) = 2 + cos(t) over the interval [0, pi], we need to calculate the difference between the function values at the endpoints of the interval and divide it by the difference between the endpoints.
So, let's begin by calculating g(pi) and g(0):
g(pi) = 2 + cos(pi) = 2 + (-1) = 1
g(0) = 2 + cos(0) = 2 + 1 = 3
Now, we can determine the average rate of change:
Average rate of change = (g(pi) - g(0)) / (pi - 0)
= (1 - 3) / pi
= -2 / pi
So, the average rate of change of g(t) over the interval [0, pi] is -2/pi.
To find the average rate of change of the function g(t) = 2 + cos(t) over the interval [0, pi], you can follow these steps:
Step 1: Find the value of the function at the endpoints of the interval.
Plug in the values of 0 and pi into the function g(t) to find the corresponding y-values.
g(0) = 2 + cos(0) = 2 + 1 = 3
g(pi) = 2 + cos(pi) = 2 - 1 = 1
Step 2: Calculate the change in the y-values.
Subtract the y-value at the starting point from the y-value at the ending point.
Change in y = g(pi) - g(0) = 1 - 3 = -2
Step 3: Calculate the change in the x-values.
Subtract the value of the starting point from the value of the ending point.
Change in x = pi - 0 = pi
Step 4: Calculate the average rate of change.
Divide the change in y by the change in x.
Average rate of change = Change in y / Change in x = -2 / pi
Therefore, the average rate of change of the function g(t) over the interval [0, pi] is -2/pi.
Yes, I can help you find the average rate of change of the function g(t) = 2 + cos(t) over the interval [0, pi].
To find the average rate of change, we need to calculate the change in the function's values over the interval and divide it by the change in the input values.
Step 1: Calculate the change in the function's values.
Substitute the upper limit (pi) and the lower limit (0) into the function g(t).
g(pi) = 2 + cos(pi) = 2 + (-1) = 1
g(0) = 2 + cos(0) = 2 + 1 = 3
The change in the function's values is g(pi) - g(0) = 1 - 3 = -2.
Step 2: Calculate the change in the input values.
The change in the input values is pi - 0 = pi.
Step 3: Calculate the average rate of change.
Divide the change in the function's values (-2) by the change in the input values (pi).
Average rate of change = (-2) / pi ≈ -0.636
Therefore, the average rate of change of the function g(t) = 2 + cos(t) over the interval [0, pi] is approximately -0.636.