1MC3 Assignment #6 1. Evaluate the following limits: (a) lim- V.x - 6 (b ) lim 2-Vx+2 4 - x (c) lim (d) lim sin 3x (Hint: lim sin x -=1) 1-+36 x -36 1-$2 x-2 x+2 3- Vx3 + 5 x-0 tan 5x x-0 x 3 2. Determine the values of x for which the following function is continuous: y = x- + 4x Find its asymptotes. - x 3. Explain why the given function is discontinuous at x = 1: f(x) = x =1 4. Find the equation of the tangent and the normal lines to the curve y = 4 at the point (4,1). 5. A ball is thrown upward in the air with a velocity of 12 m/s and its height after / seconds is given by h =121 -4.912. Use Calculus methods to determine the following: a. Find the velocity when ? = 2 s. b. When will the ball hit the ground? c. With what velocity will the ball hit the ground? 6. If the tangent line to y = f (x) at (2, 4) passes through the point (5,10), find f(2) and f'(2) . 7. Differentiate: a. f(1) = -4+1 b. f(x) =5" c. y=(Vx+1).(e*) d. f(x) =e'sin 2x-x'cos 3x 8. Find the second derivative of f(x) = In(xe-5x)