Determine whether the following statements are true or false. If true, provide justification. If false, provide a counterexample i.e. an example that shows that it is possible for the hypothesis of the statement to be satisfied, but not the conclusion. You may choose to give an algebraic expressions or graphs as counterexamples. (a) If f(1) = 2, then lim f(x) = 2. x→1 f(x) x>0 g(x) (c) If lim f(x) exists and lim f(x) exists, then lim f(x) exists. (b) If lim g(x) = 0, then lim does not exist. x→0 x→0- x→0+

f(x) = x* + x³ – 2x? | For the above function state all intervals of x where f(x) is negative.

A state charges polluters an annual fee of $10 per ton for each ton of pollutant emitted into the atmosphere, up to a maximum of 3,000 tons. No for are charged for emissions beyond the 3,000-ton limit. Write a piecewise definition of the fees F(x) charged for the emission of x tores of pollutant in a year What is the limit of For) approaches 8,000 tons? approaches 3,000 tons? As x Write the piecewise definition of the fees F(x) charged for the emission of x tons of pollutant in a year #0 3,000 (Simplify your answers.) Find the limit of F(x) as x approaches 3,000 tons. Select the corect choice below and, if necessary, fill in the answer box to complete your choice (Type an integer or a decimal) F(x)= OA Tim F(x)-S *-+3,000 OB. The limit does not exist Find the limit of F(x) as x approaches 8,000 tons. Select the correct choice below and, if necessary, fill in the answer box to complete your choice OA im F(x)-$ (Type an integer or a decimal) x-8.000 Time Remaining: 00.58 12 Next