Show all your work and box the answers. 1. Find the derivative of the function using the definition of derivative (the limit). Do not use the differentiation formulas. State the domain of the function and the domain of its derivative in interval notation. Show all your work and do not skip steps. g'(X): Domain of g(x): Domain of g'(x): 2. Differentiate using the differentiation formulas and simplify your answer. Show all your work. a). 4 = 7 VI + 1 b). g(x) = Vx(x +2Vx) COST C.) y = ] - sinc d). h(0) = tan(02 sin 0) [Hint: Use the Chain Rule]3. Find the equations of the tangent line and normal line to the curve at the specified point. Write both equations in the slope-intercept form. Show all your steps. x2 1 2xy | 4y' - 12, (1, 2) Equation of the tangent linc: Equation of the normal line 4. Find the limit. Show all your steps. lim I - secr arch Roster -Matic 5. Find # by implicit differentiation. Show all your steps. y sin (r?) = x sin (y? ) 6. For the following word problem draw the diagram to answer the question posed in the problem. Show all your work. A kite 100 ft above the ground moves horizontally at a speed of 8ft/s. At what rate is the angle between the string and the horizontal decreasing when 200 ft of string has been let out. 7. Use a lincarization (or differentials) to estimate the given number. Show all your work. V 100.5