Let P(3,4) be a point on the circle x2 + y2 = 25.

Question

calculate the Lim Mx as x approaches 3. How does this number relate to your answer in part b?
Part b the answer was to find the slope Mx of the line joining P and Q which is M=4-(root(25-x2))/3-x.

Answer 1

lim (x->3) 4-(√(25-x2))/(3-x)
Use l'Hospital's Rule to get
= lim (x->3) (x/√(25-x^2)]/(-1)
= (3/4)/(-1)
= -3/4

Recall that dy/dx at any point on the circle is -x/y