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Test 1(Show all work) 1. Use the graph of f at right to evaluate the following limits. a. lim f (x) b. limf (x) c. lim f (x) x - 2 2. If a function fis continuous at x = a (i.e., there is no "break" in the graph of f at x = a), then lim f(x) = f(a). Evaluating a limit in this way is called "direct substitution." Evaluate the following limit by direct substitution: lim (2x2 -3x+5) 3. Evaluate lim f ( x th) J (x for f(x) = Vx h - 0 hx - x2 - 2 4. lim. - 2x2 5. Describe the discontinuities of the function below: specify as jump, removable or infinite. -1- -2- - 3-6. For the following exercise, determine the point(s), if any, at which each function is discontinuous. Classify any discontinuity as jump, removable or x+3 innite. f(X) = m 2x28 x2 16 7. Find the asymptotes (horizontal or vertical, and the intercepts: y = x8 3x+4 8. Find the slope ofthe secant line. f(X) = x1 : 2, X2 : 0 9. Using the definition of a derivative, find the slope of the tangent line f(x) = 1- x - x2. x= 2 10. Use the definition of derivative to find f'(x) when f(x) = Vx - 6 1 1.Does the IVT apply? If the theorem applies, find the guaranteed value of c. Otherwise, explain why the theorem does not apply. f(x) =x -4x+1 on the interval [3, 7], N = 10.12. Find the derivative of the polynomial function: f(x) : 7x3 7 5X + 8 x2 +4x+3 x/E 13.Find the derivative of the following function: x) 2 xa x