Calculus I limits// Limits and instantaneous rate of change.

Question

Please I need help!! Limits and instantaneous rate of change.

The point P(16,6) lies on the curve y=√x+2.

If Q is the point (x,√x+2), find the slope of the secant line PQ for the following values of x.

If x=16.1, the slope of PQ is:

If X=16.01, the slope of PQ is:

If X=15.9 the slope of PQ is:

If X15.99, the slope of PQ is:

Based on the above results, guess the instantaneous rate of change of y=√x+2 at P(16,6).

This is a math exercise, limits and change of rate. Thank you so much for your help.

Answer 1

Nathalia

If f(x) = √x + 2

P is (16,6)

When x = 16.1, Q = (16.1, √16.1 + 2)

Slope PQ = change in y from P to Q / change in x from P to Q so

√ 16.1 + 2 - 6 / (16.1 - 16) = 0.1248

x = 16.01 Q = (16.01, √16.01 + 2)

Slope PQ = √ 16.01 + 2 - 6 / (16.01 - 16) = 0.1250

etc

As the point Q gets closer to P on the right hand side the slope will approach the slope of the tangent line on the right hand side.

Try the others yourself !

Mike