1. Complete the following: a) b) c) d) e) f) The lim -4x = X-3 The...

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1. Complete the following: a) b) c) d) e) f) The lim -4x = X-3 The lim x - 16 = x -4+ The lim 4-x X 0 X The lim 2 9- x' x3 x-3 = For what values of x will the function f(x) = x+2 x3-2x-8x be discontinuous? Even if a function has a removeable discontinuity at x = a, then the limit as x a can still exist at x = a. Is this statement T or F? Explain your answer. 3. Sketch a diagram for Instantaneous Rate of Change and explain the formula. Create a real-life example. 4. Discus the continuity/disconutity of the following graph. y 1 Ax -1 -1 X 5. a) Determine the value(s) of k for the following limit to exist. If you find any values for k, then state value of the limit L. If this question has no solution explain why it doesn't. Show rough work. L = lim x+kx-6 x1 x+1 6. Find values of a and b so that the following function is continuous. x + 3x + 2 x + 1 f(x) = ax -X + bx + 5 - 3 if x < 1 if1 x 1 if x > 1 In order for f(x) to be continuous, a must equal and b must equal 8. a) Evaluate these limits algebraically showing all the steps. If it does not exist explain why. [2,2,3,3] x-2 lim x-24-x b) lim (x-31 x 3 9. a) 5-x Consider f(x) = and use, mtangent x-3 f(x+h)-f(x) = lim to determine the h0 h simplified expression in terms of x for the slope of any tangent to f(x) and state the slope at x = 1. 1. Complete the following: a) b) c) d) e) f) The lim -4x = X-3 The lim x - 16 = x -4+ The lim 4-x X 0 X The lim 2 9- x' x3 x-3 = For what values of x will the function f(x) = x+2 x3-2x-8x be discontinuous? Even if a function has a removeable discontinuity at x = a, then the limit as x a can still exist at x = a. Is this statement T or F? Explain your answer. 3. Sketch a diagram for Instantaneous Rate of Change and explain the formula. Create a real-life example. 4. Discus the continuity/disconutity of the following graph. y 1 Ax -1 -1 X 5. a) Determine the value(s) of k for the following limit to exist. If you find any values for k, then state value of the limit L. If this question has no solution explain why it doesn't. Show rough work. L = lim x+kx-6 x1 x+1 6. Find values of a and b so that the following function is continuous. x + 3x + 2 x + 1 f(x) = ax -X + bx + 5 - 3 if x < 1 if1 x 1 if x > 1 In order for f(x) to be continuous, a must equal and b must equal 8. a) Evaluate these limits algebraically showing all the steps. If it does not exist explain why. [2,2,3,3] x-2 lim x-24-x b) lim (x-31 x 3 9. a) 5-x Consider f(x) = and use, mtangent x-3 f(x+h)-f(x) = lim to determine the h0 h simplified expression in terms of x for the slope of any tangent to f(x) and state the slope at x = 1.