Consider the function f(x) = Vx - 3. (a) Simplify the following difference quotient as much as possible f(x + h) - f(x) = h 1/(sqrt(x+h-3)+sqrt(x-3)) (b) Use your result from (a) and the limit definition of the derivative to calculate df lim f(x + h) - f(x) E dx h +0 h 1/(2sqrt(x-3)) (c) Use your answer from part (b) to find the instantaneous rate of change of f(x) at x = 28. Answer: 1/10 E (d) Find the equation of the tangent line to the curve at the point (28, f(28)). ELet f(t) = 2 t+4 (a) Simplify the following difference quotient as much as possible f ( t + h) - f(t) h (b) Use your result from (a) and the limit definition of the derivative to calculate f' (t) = lim f (t + h) - f(t) h 0 h (c) Use your answer from part (b) to evaluate f' (1) = E (d) Find the equation of the tangent line to the curve at the point (1, f(1)). V = El[Zoneiderthe function at} 2 Sq? 1. {a} Slrnpllf],r the following difference quotient as much as possible as: + ht are} 2 h E {D} Use your result from {a} and the limit definition of the derivative to calculate ma 2 lie awn; first = E {c} Use your anewer from part {b} to evaluate 3"[15] = E {de Find the equation of the tangent line to the curve at the point [1E f{ 16]}. 1v= E Let r(t) = t. (a) Simplify the following difference quotient as much as possible r(t t h) - r(t) E h (b) Use your result from (a) and the limit definition of the derivative to calculate r'(t) = lim r (t t h) - r(t) M h (c) Use your answer from part (b) to evaluate T'(1) E (d) Find the equation of the tangent line to the curve at the point (1, r(1)). y =