Active Calculus - Gvsu - Grand Valley State University

2.8. USING DERIVATIVES TO EVALUATE LIMITS 63Activity 2.23.In this activity, we reason graphically to evaluate limits of ratios of functions about which someinformation is known.2gf212 p 1q1r1 2 3 41 2 3 41 2 3 4-1-1-1-2-2-2sFigure 2.6: Three graphs referenced in the questions of Activity 2.23.(a) Use the left-hand graph to determine the values of f(2), f ′ (2), g(2), and g ′ (2). Then,evaluatef(x)limx→2 g(x) .(b) Use the middle graph to find p(2), p ′ (2), q(2), and q ′ (2). Then, determine the value ofp(x)limx→2 q(x) .(c) Use the right-hand graph to compute r(2), r ′ (2), s(2), s ′ (2). Explain why you cannotdetermine the exact value ofr(x)limx→2 s(x)without further information being provided, but that you can determine the sign ofr(x)lim x→2 s(x). In addition, state what the sign of the limit will be, with justification.⊳