Please kindly solve all of the following questions. Thanks!

Use the difference quotient method to determine the equation of the tangent to the graph of (x) = x2 -2x+13 where x = 3. (A -4 marks) 3) For the graph of y = f(x) shown below, determine each of the following limits. (A - 4 marks) a) lim f (x) = x-+2- b) lim f (x) = X - 2 + c) lim f (x) = x-+2 - N d) lim f (x) = x -+ 0 4) As a snowball melts, it's volume decreases. The volume in cubic centimetres is given by the equation V(r) = - , where r is the radius in centimetres. Determine, to the nearest tenth, the rate of change of the snowball's volume when its radius is 10 cm. (A -4 marks)5) The total cost, in dollars, of manufacturing x calculators is given by (I -6 marks) C(x) = 10Vx + 1000. a. What is the total cost of manufacturing 100 calculators? b. What is the rate of change in the total cost with respect to the number of calculators, x, being produced when x = 100? 6) Evaluate each limit, using a table of values. If the limit does not exist, explain why. (a) lim (x3 -1) (1-6 marks) b) lim x+0 xA weather balloon is rising vertically. After t hours, its distance above the 7 ) ground, measured in kilometres, is given by the formula s(t) = 8t - 12. a. Determine the average velocity of the weather balloon from t = 2 h to 1 = 5h. L. (C -3 marks) b. Determine its velocity at t = 3 h. 8) A few days after their intense conversation about limits, Jenny and Karlo went on a date. While they were enjoying their meal, Jenny told Karlo that the expression J (xx) - f(5) ; is the x - 5 slope of the tangent line to f (x) at the point where x = 5. Is Jenny's claim correct? Explain. (C-3 marks)