The Point $P ( 1 , \sqrt { 3 ) }$

Essay

The point $P ( 1 , \sqrt { 3 ) }$ lies on the curve $y = \sqrt { 4 - x ^ { 2 } }$ Let Q be the point $\left( x , \sqrt { 4 - x ^ { 2 } } \right)$ (a) What is the slope of the secant line PQ (correct to 6 decimal places) for the following values of x?
(i) 2
(ii) 1.5
(iii) 1.1
(iv) 1.01
(v) 1.001
(vi) 0
(vii) 0.5
(viii) 0.9
(ix) 0.99
(x) 0.999
(b) Use your results from part (a) to estimate the slope of the tangent line to the graph of $y = \sqrt { 4 - x ^ { 2 } \text { at } x = 1 }$