4. Is it possible that there exists some function g(x) and some constant L such that lim g(x) = lim g(x) = L, but lim g(x) does not exist? If so, draw a sketch of such a x-2+ x-2 function. If no, explain why not.

Q: Re Prove directly from definition that it f is a positive function so that lim +(x)=16, then…

A:

Q: 3) Sketch the graph of a function that has all of the following properties. lim f(x) = ∞ x→-3 ● ●…

A: Given that,

Q: -4+x, x)= {=-x if x 2 3 if x 3 Evaluate the following expressions. lim f(x) = x-3 lim f(x) = x-3+…

A: f(x)=-4+x,    if x<3   2-x,    if x⩾3 now I am attaching image so that you can easily understand…

Q: Show by example that lim[f(x) +g(x)] can exist even if lim f(x) and lim g(x) do not exist.

A: Let,  f(x)=1x-c, g(x)=1c-x

Q: If 2x < g(x) < x* – x² + 2 for all x, find lim g(x). x-1

A:

Q: 1) Sketch a graph of a function that has the following properties: lim f(x) = -2 lim, f(x) = 1 f(3)…

A: We can use the concept of graph in order to solve the given problem.

Q: If f is a function such that f(2)=4,can you conclude anything about lim as x tends to 2 for the…

A: The objective of the question is to understand if we can conclude anything about the limit of a…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.