Solve the problem.What conditions, when present, are sufficient to conclude that a function f(x) has a limit as x approaches some value of a?

A. f(a) exists, the limit of  as  from the left exists, and the limit of  as  from the right exists.
B. The limit of  as  from the left exists, the limit of  as  from the right exists, and these two limits are the same.
C. Either the limit of  as  from the left exists or the limit of  as  from the right exists
D. The limit of  as  from the left exists, the limit of  as  from the right exists, and at least one of these limits is the same as f(a).


Answer: B

Mathematics

You might also like to view...

Use a graphing calculator to find the vertex of the graph of the function.f(x) = 4x2 - x + 6

A. (-0.125, 5.9375) B. (0.125, 6.0625) C. (0.125, 5.9375) D. (0.125, 6)

Mathematics

Solve the problem.Suppose that the total annual consumption of salmon in a certain country is given by  and that the total annual consumption of tuna in this country is given by , where consumption is measured in millions of pounds and x is the number of years since 2010. Find the year in which consumption of salmon reaches consumption of tuna.

A. 2027 B. 2025 C. 2023 D. 2028

Mathematics

Expand the expression using the Binomial Theorem.(3x2 - 1)3

A. 81x8 + 27x6 - 27x4 + 9x2 - 1 B. 27x6 - 27x4 + 9x2 - 1 C. (9x4 - 6x2 + 1)3 D. 27x3 - 27x2 + 9x - 1

Mathematics

Use the properties of inverse trigonometric functions to evaluate .

A.
B.
C.
D.
E.

Mathematics