1. Find each limit. 2x2+1 b) limx-2- x2-3x+2 a) limx-2 3x2-4 X2 -4 x2+2x+1 d) limp-0 (2+h)3-8 c) limx--17 x3+1 h e) limn-o (3 +h) 2 9 x2 -x-6 h f) limx--2 2x2+5x+2 2. Let -x -2 ifx2 a) Find the following limits, if they exist. i. limx--2- f (x) ii. limx--2+ f (x) iii. limx--2 f (x) iv . limx-+2- f (x) V . limx-+2+ f (x) vi. limx-2 f (x) b) Sketch the graph of f(x). c) Where is f(x) discontinuous? d) Where is f(x) not differentiable? 3. Find the following Limits. 1-2n3 a) limn-+0o n+13 b) limn-+0 3-n 4. If f (x) = 6- 5x + 3x2, find f'(x) using the first principle. 5. Find the equation of the tangent line to the parabola y = 6 - 5x + 3x2 at the point where x = 1. 6. Find the derivative of the function g (x) = v3 - x using the first principle. 7. Differentiate. a) f(x) = 12x5 -2x4 - 4x b) f (x ) = - c) g(x) = Vx (2x + !) d) g(x) = - x 2 2 x - 3 e) f(t) = V2t -t3 f) f ( y ) =zy 1+2y g) f (x) = (3x + 5)(x3 - 1)3 h) f (x) =; 1 5x5+1 i) f (x ) = Vx - x X x2 i) f (x ) = 1+ x2