ASSIGNMENT 2 - CONTINUITY/ LIMITS INVOLVING INFINITY/ STARTING DIFFERENTIATION Please hand in your assignment by noon October 3rd at the latest. Please hand in either by slipping under the door of my office if I'm not in, or by placing your work in my 'cubby-hole' in the A-wing corridor. Please make sure you make your working clear and highlight/ box your final answer. 1. Evaluate the following limits: 6pt (a) lim 4 x-+2 (b) lim 2x X-+2 (c) lim - x-+2 x +1 (d) lim x- - 4 x -+2 x - 2 (e) lim - V12 + 9 -3 +2 (f) lim x2 - 7x + 10 x - 2 (g) lim - Vx +h- Vx h-+ 2. Evaluate the following limits involving infinity: 6pt (a) lim - 1-x2 X-14 X2 - 16 (b) 1 - x3 x-+0% 2x2 - 7 (c) lim 1-x-x2 -100 2x2 - 7 (d) lim [x* + x] (e) lim Vx2 - 4 1 + 00 x + 1 (f ) lim vx2 + ax - Vx2 + bx 3. Assume that constant a is positive. Find equations for all horizontal and vertical asymptotes for the graph of f(x) = Vax- + 4 x - b 3pt 4. Find the formula for a single function f(x) that satisfies all the following conditions: 3pt (a) limx-+to f(x) = 0 (b) limx-to f(x) = -00 (c) limx-3- f(x) = 00 (d) limx-3+ f(x) = -0o (e) f(2) = 0 This one is a toughy :) 5. Find the derivative of the function f(x) = 3x - x by using the definition of the derivative and use the derivative to find the equation of the tangent line at the point P(-1,4) 3pt 6. Find the slant asymptote of f(x) = 2pt 7. Differentiate: 4pt (a) f(x) = (2x3 + 3)(x" - 2x) ( b) f ( x) = Vx3 (c) f ( 7 ) = 17 (d) f( x) = xHE Where c is a constant. You do not need to simplify any solutions. 8. Differentiate: 4pt (a) y = tan'(sec? (x*)) (b) y = sec(0)tan(0) (c) y = sec[e) 1+sec(@) (d) y = cot'(sin(0))