Show complete solution and use proper notations. - PROVIDE JUSTIFICATION for answers that might not need a solution. (e.g. 1/0 is undefined since the denominator cannot be zero).

1. (1 pt) Evaluate the limit: lim vx - 19 2. (2 pts) Solve for m s.t. the function is continuous (Do not use L'Hospital's Rule and Do not use shortcuts) x+3 *#-3 f(x) = x2 - 9 (2 - my * = -3 3. (8 pts) Given the function, g(x) 4 3x - 5 g(x) = 15x53 x - x>3 a. Determine the possible points of discontinuity. b. Discuss the continuity/ discontinuity of the function at the points determined in (a). 4. (3 pts) Determine _ given: axlys - In(x*y') = bx+ y where a and b are constants. 5. (4 pts) Verify Young's Theorem z = In(x + 2y) + -+ e (2x+y) X 6. (5pts) Given the function f(x) = x3 + x2 - x + 5, using the method shown in class, a. (2pts) Discuss the direction of the function at x = = = b. (3pts) Discuss the direction and concavity of the function at x = 0 7. (3 pts) Evaluate the following limit using L'Hospital's Rule, when applicable: V9m + 3 2m2 lim m- V16m +4 3m= + 1