Exercise 4.1.1 Draw the graph ofthemction y = f(x) = v\" 169 JI:2 between I = Bands = 13. Find the slope city/Ax of the seeant line between the points ofthe circle lying over (a) x = 12 and x = 13. {b} x = 12 andx = 12.1, {a}: =12 and): =12.01,(d).r =12 andx =12.001. Now use the geometry oftangent lines on a circle to nd (e) the exact value of the derivative (12). Your answers to (aHtl) should be getting I closer and closer to your answer to f e ,1. Exercise 4.1.4 Find an algebraic expression for the difference quotient (l + Ax) f{1))fh.x when f(x} = J:2 (l/x). Simplir the expression as patch as possible. Then determine what happens as Ax approaches 0. That value is f' (1}. Exercise 4.1.5 Draw the graph ofy = f(x) = 13 between I = 0 and I = 1.5. Find the slope of the seoant line between (a) x =1and x = 1.1, (b) x =1ana'x = 1.001, (e) x =1 and x =1.00001. Then use algebra to nd a simple formula for the slope of the secant line between 1 and l +1.17. ( Use the expansion (A +3)3 = A3 + 3:423 + 311132 +33.) Determine what happens as A: approaches 0'. and in your graph of y = x3 draw the straight line through the point {1, 1} whose slope is equal to the value you just found