MATH 1004, Section B & E Due 16 October, 2017 (at the beginning of tutorial) ASSIGNMENT 1 1. Evaluate the following limits x3 x x1 x 1 ex (b) x lim 3 x (a) lim (c) lim q t/4 | sin(t)| Hint: sin(/4) = 2 2 (d) lim tan(h) h s2 + 1 (e) lim s+ s 117 2. Does the following limit exist? Explain your answer clearly. lim x. x0 Hint: evaluate the left and the right limit. 3. Consider the following function: f (x) = 9 x2 , which is defined on [3, 3]. (a) Is f continuous, or just left continuous, or just right continuous at x = 3? why? (b) Is f continuous, or just left continuous, or just right continuous at x = 3? why? 4. Determine at what point(s) the following functions are discontinuous. 1 x2 2 |x 1| (b) f (x) = 2 x 1 (a) f (x) = 5. Differentiate the following functions: (a) f (x) = x(3x2 + 1) x3 1 x2 + x + 1 (c) f (x) = sec(x3 + x) (b) f (x) = (d) f (x) = cos1 (3x2 + tan(x3 )) 6. Evaluate the following limits when they exist. When the limit does not exist explain why. sin x , x3 sin x (b) lim 2 , x0 x limits. (a) lim x0 Hint: Use the L'Hopital's rule. Hint: First use the L'Hopital's rule and then obtain the left and right