Evaluate the function f(x) at the given numbers (correct to six decimal places). f(x) = x2 − 7x x2 − 6x − 7 , x = 0, −0.5, −0.9, −0.95, −0.99, −0.999, −2, −1.5, −1.1, −1.01, −1.001 f(0) = f(−0.5) = f(−0.9) = f(−0.95) = f(−0.99) = f(−0.999) = f(−2) = f(−1.5) = f(−1.1) = f(−1.01) = f(−1.001) = Guess the value of the limit of f(x) as x approaches −1, correct to six decimal places. (If an answer does not exist, enter DNE.) lim x→−1 x2 − 7x x2 − 6x − 7 =

Step-by-step explanation:

From the given information:

We are given the function:

when x = 0;

f(0) = 0

when x = -0.5

when x = -0.9

when x = -0.95

when x = -0.99

when x = -0.999

when x = -2

when x = -1.5

when x =  -1.1

when x = -1.01

when x = -1.001

So, if we make a table to show the correlation for the values of  x and corresponding f(x) and also include the value of -1 whose limit of f(x) is unknown, we have;

x          0       -0.5       -0.9       -0.95        -0.99         -0.999       -1

f(x)       0       -1            -9        -19               -99               -999       ????

x         -1.001        -1.01              -1.1              -2

f(x)       1001           101               11                 2

From the table above, we can see that for x values ranging from 0 → 999, f(x) values decline from 0 to ∞, while f(x) values increase from -2 →  -1.001 towards ∞.

As the value of (x) declines from left to right and increases from right to left towards -1, we may assume that f(x) reaches - ∞ and + ∞, accordingly.

∴

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,