B4 18:20 X H D ... 69 Question 1: (4 Marks) In the expansion of (ax2 -" ) in descending powers of x, the coefficients of the 3"d term and the x term are 112 and -448, respectively. Find a and b. Question 2: (4 Marks) Solve the equation In(3x - 1) + In(2x + 1) = 0 for x. Question 3: (4 Marks) Find lim - 4x2-4 x-1 Vx2+2-V3 Question 4: (4 Marks) Find lim 4x5-2x2 x-00 5x5+5 Question 5: (4 Marks) The first derivative of y = (3x2+1)2 can be written as (3x2 + 1)(bx2 - cx - d)(2x -1)e . (2x-1)2 Find a, b, c, d and e. Question 6: (4 Marks) Given that the slope of f (x) = Inle-*(x2 + c)] at the point (0,0) is equal to k, determine the values of and hence k. (Hint: Recall that a point (a, b) lies on the graph of a function f (x) if and only if f (a) = b. ) Question 7: (4 Marks) Based on your solution in Question 6, use the first derivative test to find the maximum or minimum point(s) of f (x). Question 8: (4 Marks) Evaluate the following indefinite integral: 1 (esx - 2 ) ax. Question 9: (4 Marks) Evaluate the following indefinite integral using the method of substitution: 5 x3 ex* dx. Question 10: (4 Marks) Evaluate the following indefinite integral using integration by parts: xV5x + 6 dx. ~End of Assignment~