What is the slope of the line through (2,4) and (x, y) for y = x2 + x - 2 and x=1.99? x=2.004? x=2+h. what happens to this last slope when h is very small?

Part 1)

Part 2)

Part 3)

Part 4) The slope tends to 5.

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

we have

the points (2,4) and (x,y)

Part 1)

For x=1.99

substitute the value of x in the quadratic equation and solve for y

we have the points

(1.99,3.9501) and (2,4)

substitute the values in the formula of slope

Part 2)

For x=2.004

substitute the value of x in the quadratic equation and solve for y

we have the points

 (2,4) and (2.004,4.020016)

substitute the values in the formula of slope

Part 3)

For x=2+h

substitute the value of x in the quadratic equation and solve for y

we have the points

(2,4) and (2+h,h^{2}+5h+4)

substitute the values in the formula of slope

Simplify

Part 4) What happens to this last slope when h is very small

If the value of h is very small, then the value of h tends to zero and the value of m tends to 5.

therefore

any options?

step-by-step explanation: