Please help me with them, it's urgent!

1. (17 marks) Evaluate the following limits, if they exist. (a) lim 13 - 41 + 4x T-2 1 - cos(TI) (b) lim 12 +3 - V21 + 2 (x - 1)2 (c) lim e 3 cos(15 ) (d) lim (ex + 5.1 ) 21 1 T-+005. [5 marks) At What pointa] an the curve 3' = 62' + 413 + 9' is the tangent line perpendicular to the line D: + 53' = 7? 6. (8 marks) A rectangular beam will be cut from a cylindrical log of radius 10 inches Suppose that the strength of a rectangular beam is equal to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from the cylindrical log. 7. (16 marks) Let f(x) = x4/3 - 2x1/3 (a) (1 Mark) State the domain of f. (b) (3 Marks) Find the x and y intercepts (if any). (c) (4 Marks) Find the intervals of increase/decrease of f, given that f ( x) = 4x - 2 3 x2/3(d) (2 Marks} Find local minimum and local maximum values of f {if any}. 4x+4 3.' 3 (e) (4 Marks) Find the intervals of concavity of f. given mat f GEE) = \f8. (8 marks) Let A be the area of the region that lies under the graph of f(x) = 2x' + 7 between x = 0 and x = 2. Find expression for A as a limit using right endpoints. Evaluate the limit without using the Fundamental Theorem of Calculus. (No marks will be given for finding the area by any other method)