Prove that the function |2x - f(x) = 32x3 6-4x does not tend to a limit as x tends to 3. Use the e- definition of continuity to prove that the function f(x) = x3 + x²-4x is continuous at the point c = 2. Prove that the function f(x) = x-2 2x+1 is uniformly continuous on the interval [1, 3], referring to any results from the module that you use.

Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.

Determine whether fx=x is one-to-one.

XELVT US ƏəIf XFivI subs O Find the value(s) of a and b for which f is continuous at -2: if x -2 f(x) =

Determine if the function is continuous or discontinuous at x = -4 using the three step continuity checklist. 1) x + 6 x -4 -

Which of the following choices correctly discusses the continuity of the following function? F(x)= (x+3)/(x^2-9) A. F(x)is continuous on (neg. infinity, -3)U (-3,3)U (3, infinity). F(x) has a removable discontinuity at (3,1/6) and a nonremovable discontinuity at x=-3. B. F(x) is continuous on (neg. infinity, 3)U (3,infinity). F(x) has nonremovable discontinuity at x=3. C.F(x) is continuous on (neg. infinity, -3)U (-3,3)U (3, infinity). F(X) has nonremovable discontinuity at x=3 and a removable discontinuity at (-3,-1/6). D. F(x) is continuous on (neg. infinity, -3)U (-3,infinity). F(x) has nonremovable discontinuity at x=-3.

Determine the whether the function is continuous at x=-2. Justify your answer 2x+7 if xS-2 using the definition of continuity. f(x)={ x² -1 if -22

21) Write a function that has an infinite discontinuity at x = 100. 22) Write a function that is continuous over (-∞, 0), (0, 1), and (1, ∞) and discontinuous everywhere else.

Use the definition of continuity, along with the One- sided continuity theorem, to determine whether the following function is continous at x=4. Also discuss whether the function is left-continuous and/ or right-continous at 4. f(x)={3                 if x=4        {|3x-12|/x-4  if x not equal to 4 Refering to  graph or a table of value will earn zero credit.