Consider the graph of the function f(x)=x³-12x² +27x/x²-9x

If f x exe 8 and g x f x lim x 0 g x 2x then Your answer needs to be in exact form Your written work should use calculus methods to find the limit and inlcude a justification for why you are able to use those methods

The graph below shows the profit P from the daily production of x thousand kilograms of an industrial disinfectant Use the graph to complete parts a through f to the right leinuen und unt 2000 1500 1000 P x 500 0 10 1400 First shift Second shift 10 900 56 10 15 of units 1000s of kilos 20 N a Find lim P x Select the correct choice below and if X 6 necessary fill in the answer box within your choice OA lim P x X 6 Round to the nearest hundred as needed limit does not exist OB lim P x X 6 C The limit lim P x does not exist because the X 6 one sided limits are not equal

The amount of income tax t an individual owes is defined by piecewise function t and is based on the individual s income where is taxable income in dollar 0 10 t i 755 0 12 11000 4500 b i 35000 if Osis 12 000 if 12 000 32 000 if 32 000 Part A Show that the function t is not continuous at 12 000 10 points Part B Find the value of constant b that makes t i continuous at 32 000 20 points

2 1 0 1 2 3 4 8 x values 6 b Find X 2 2 g x values Limit values of g x x 2 4 1 2 1 c If f x x 2x and 4 0 lim g x 5 lim g x 0 2 5 3 a Use the graph of f and the table of g to determine lim f x 4 lim X 6 lim g x 2 lim g x 2 x 6 x 5 x 1 1 then find x 2 6 2 lim f x g x 6 2f x 2 3 f g x according to limit theorems 3 points or explain why it does not exist Use correct limit notation in your answer 3 points g x 8 Justify your answer and use correct limit notation in your work 41

Find all points where the function is discontinuous. A. None B. x=2 C. x = 4 D. x = 4, x = 2

Let f(x) = -8 - 5/x+16 Complete the tables below. Round all table values to four decimal places, if necessary. Enter DNE if a function value is undefined. Using the data in the tables above, determine the following limits. Enter DNE if a limit fails to exist, except in case of an infinite limit. If an infinite limit exists, enter ∞ or -∞, as appropriate.

Let f(x)=√x6 +5x - x³ - 3. Complete the tables below. Round all table values to four decimal places, if necessary. Enter DNE if a function value is undefined. Using the data in the tables above, determine the following limits. Enter DNE if a limit fails to exist, except in case of an infinite limit. If an infinite limit exists, enter ∞ or -∞, as appropriate.

(1 point) Find an integer which is the limit of tan(8x)/2x as x goes to 0. (Enter I for infinity or DNE for does not exist.)

Use a graph or table of values near x =π/2 to estimate the value of this limit: lim x - 72 cos(7x)/x-π/2 i

Let f be the function defined as f(x)= 3 for x<5 x+7 for x≥ 5 Which of the following statements is true? f is not differentiable at x = 5 because f is not defined at x = 5. f is not differentiable at x = 5 because fis not continuous at x = 5. f is not differentiable at x = 5 because the graph off has a vertical tangent at x = 5. f is not differentiable at x = 5 because the graph of f has a cusp at x = 5.