9:46 a) y=(x²+2)Inx² d) f(x) = (4x²-3x+8)* Calculus Culminating Task Part A: Knowledge and Understanding 1. Find the derivative for each function below. Use which ever differentiation rule you wish. It is only necessary to show the first step. Watch your notation. √x+1-1 x smileldcsbon-my.sharepoint.com ED Info | f(x)=4-x², if x<1 2x+1, if x21 f(x)= 3 b) y=(2¹-x)³¹ 2. Evaluate the limits of the functions below. If the limit doesn't exist, write DNE. Justify your answers. a) lim b) lim c) lim x²+12x+32 x+4 Part B: Application 4. Find the equation of the tangent line to the given curve at x = 1. 3. Given the piecewise function, determine if the function is continuous at x = 1. Justify your answer. DI LTE O c) y = ²x 2cosx e) f(x) = (4x-6)³(-2x² + 6x-10)* the disease is approximated by P(1) 20 - for Osts 20. = 1000 + 5. A company wants to manufacture cylindrical aluminium cans with a volume of 1000 cm³. Determine the radius and height of the can that will minimize the amount of aluminium used. Decimals to one decimal place are permitted. 6. Epidemiologists have found a new communicable disease running rampant in a city. They estimate that t days after the disease is first observed in the community, the percent, P, of the population infected by X :) : ...