Consider the curve x sin(xy - y2) = x 1. (a) dy dx (b) 913 dx dy

Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.

True or false. if false, correct statement. if true, explain why.  a. if a function, f, is continuous at a point c, then f is differentiable at the point c. b. if a function is concave down on its domain, then it will have a relative maximum. c. The derivative of a sum is the sum of its derivatives. d. the derivative of a function, f(x), is equal to limh->0 (f(x+h)-f(x))/h for all x values in the domain e. if f has an absolute minimum at c, then f'(c)=0