MATH 1C: Review Assignment Quiz #1 Due: Friday, Sep All work should be done on separate paper and all answers/results should be justified with work or stat Solve the initial value problem. [Find the function r(t)] dr =10t+sec2 t, r( - ) =4 1) dt Find the most general antiderivative. y 8 + +e- 2y dy 2) 3 y Find an antiderivative of the given function. 3) 9x2 +16x- 4- sin(x) ^ Identify why this limit is indeterminate, then find the limit using l'Hopital's rule. 2 x 4) lim 1 + x3 x 0 ^ Identify why this limit is indeterminate, then find the limit using using l'Hopital's rule. (- 5/ln x) 5) lim x x 0+ ^ Identify why this limit is indeterminate, then find the limit using using l'Hopital's rule. 2 6) lim x sin x x Graph the rational function. Show all asymptotes. Give the domain. Identify the interval(s) where the fu increasing /decreasing, and where the function is concave up/concave down. Use limits appropriately to Find all intercepts. x +4 7) y = 2 x +9x+20 Provide an appropriate response. 8) Suppose the derivative of the function = f(x) y is y'=(x - 2)2(x +6). At what points, if any, does the graph of f have a local minimum or local maximum? Justify your answer. Provide an appropriate response and justify your result. 9) An approximation to the total profit (in thousands of dollars) from the sale of x hundred thousand tires is giv by p = x3 - 15x2 + 48x+450, 0 < x < 12. A. Find the number of hundred thousands of tires that must be sold to maximize profit. B. Find the minimum profit. Assuming that=yf(x) is a differentiable function,xyfind by implicit D differentiation. 10)cos xy+x5 =y5 Find the derivative of y with respect . 11)y = ln(cos(ln )) Find the derivative of y with respect to the independent variable. 12)y =(sin t) 3 The graph of a function is given. Draw a graph of its derivative function on the given grid. (5 points) 13) Provide an appropriate response. 14)The accompanying figure shows a portion of the graph of a function that is twice at all x except at - differentiable x = p. At each of the labeled points, classify y and y as positive, negative, or zero. = p. at x Also, explain why the function is not differentiable Point a b c d e f y' y'' Answer the questions. 15)A. Does lim f(x) exist? Explain. x (- 1)+ B. Is f continuous at f(1)? Explain. If not, what type of discontinuity does it have? C. Does lim f(x) = f(- 1)? Explain. x - 1+ D. Does lim f(x) exist? If so, what is the limit? x 1 - x2 +1, 4x, f(x) = - 4, - 4x +8 1, - 1 x<0 a