MCV4U: Unit 1 Assignment #2 - Evaluating Limits Algebraically Name: Provide Full Solutions to the Following Problems. 138 1. Suppose lim f(x) = 4 and lim g(x) = - 1. Use limit properties to x- a determine the value of the limit below. [4 marks] lim 2+9(x) f(x) -29(x) x - a 2. Evaluate each using algebraic techniques. [16] a. lim 2x - 5x-3 x - 3 X - x-6 b. lim x * + 16 x+2 x - - 2 c. lim x - 6 x - 6 Vx-2-2 d. lim X 1 x - - 3 3 + x 3. For the function f(x) = x - 2+1: a. Determine f'(x) from first principles. [4] b. Determine the slope of the tangent to f(x) at x = 2. [2] c. Determine the point on the curve where the slope of the tangent is equal to -3? d. Sketch f(x). Draw the tangent lines associated with 'b', & 'c'. [4] 4. Determine the derivative of the following functions from first principles. [8] a. f ( x) = 1-x b. f (x ) = Vx + 6