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Activity 1. Now that you know the most essential terms and concepts in the study of limits and continuity of functions. Let us try to check your understanding of these terms and concepts. Kindly answer the following to deepen one's knowledge on the topic. 1. In each part, determine f'(x). (a) f(x) = V6 (b) f ( x) = V6x (c) f(x) = 6 x (d) f(x) = v6x 2. In parts (a)-(d), determine f'(x). (a) f(x) = x'+5 (b) f (x) = x- (x3 + 5) (c) f(x) = x+5 (d) f (x ) =* +5 2 x2 3. The slope of the tangent line to the curve y = x2 + 4x + 7 at x = 1 is 4. If f(x) = 3x3 - 3x2 + x + 1, then f"(x) = _ 5. A spherical balloon is being inflated. (a) Find a general formula for the instantaneous rate of change of the volume V with respect to the radius r, given that V = 4x73 (b) Find the rate of change of V with respect to r at the instant when the radius is r = 5