The point P(2, −1) lies on the curve y = 1/(1 − x). a. If Q is the point (x, 1/(1 − x)), use your calculator to find the slope of the secant line PQ (correct to six decimal places) for the following values of x:

1. 1.5
2. 1.9
3. 1.99
4. 1.999
5. 2.5
6. 2.1

b. Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(2,-1).
c. Using the slope from part (b), find an equation of the tangent line to the curve at P(2,-1).

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places

i can you with this answer

step-by-step explanation:

twenty-six miles over two gallons because the proportion for the original 13 miles to one gallon would be written 13/1 and, doing the same thing to the top and bottom, i multiplied by 2 and got 26/2