A large sphere of material is placed in a dissolving liquid. (a) When the radius is l m, it is observed to be changing at Tr" cmfhour. At that instant, what is the rate at which the sphere's volume is being dissolved with respect to time? 281'! cm3/hr X Write the first derivative of the given function. x) = ling) l?) . l?) F'TX) = x' + %.T' lnlx) v? For which xvalues does x} have horizontal tangents? (Enter your answers as a commaseparated list.) X Recall that #:(In X] = %. Also recall that the domain of In X is (0, co) and that x} has a horizontal tangent where f'fx) = 0. Use the product rule and the derivative of In X to find the derivative of the given function. Then solve (\"(X) = D to find the Xvalues where FIEX) has a horizontal tangent. What restrictions are there on the domain of ffx}? What restrictions are there on the domain of f'lbr)? Can f'fx} be factored? Are there xvalues where f'(x] = D that are not in the domain of FIX]? Suppose that uid is leaking from an overhead pipe and spreading in the shape of a circle on the ground. If the radius of the circle is increasing at a rate of 0.5 feet per minute, hOW fast is the area of the circle increasing when the radius is ? feet? 2.199 X ftZ/ m in Recall that to nd the rate at which the area of the circle changes with respect to the radius, it is necessary to find a relationship between the two quantities. Sketch the described situation and assign the variables A, r, and t to the area of the circle, the radius, and time, respectively. What is the formula relating the area of a circle and its radius? How can this relation be used to find an expression for E in terms r and ? dt dt Consider the curve ex - y = yox + 4. Using logarithmic differentiation find . Give the answer as a function of both x dx and y. dy 2y(x - Iny) = dx 2x + + 3