1. A tank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes.

T(min)

5101525V (gal)30

694444250280

(a) If P is the point (15, 250) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with t = 5,10,20,25 and 30.

(b) Estimate the slope of the tangent line at P by averaging the slopes of 2 secant lines.

(c) Use a graph of the function to estimate the slope of the tangent line at P. (This slope represents the rate at which the water is flowing from the tank after 15 minutes.)

3. The point P (1,1/2) lies on the curve y = x/(1+x).

(a) I f Q is the point (x,x/(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:

(i)0.5 (ii) )0.9 (iii)0.99 (iv) 0.999 (v) 1.5 (vi) 1.1

(b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(1, 1/2)

(c) Using the slope from part (b), find an equation of the tangent line to the curve at P (1, 1/2).

5. If a ball is thrown into the air with a velocity of 40ft/s, its height in feet t seconds later is given by y = 40t-16t^2.

(a) (i) 0.5 second (ii) 0.1 second (iii) 0.005 second

(b) Estimate the instantaneous velocity when t = 2.

I just need help from someone showing me how to do these ones. I have like 25 of them to do.