31. If f is continuous and f(3) = 9, which of the following statements must be true? (A) lim f(3x) = 9 X-3 (B) lim f(3x) = 27 X-3 (C) lim X-3 f(x) - f(3) = 9 x- 3 (D) lim Vf(x) = 3 X-3

Q: If 4.x 9 <f(x) < x² - 4x + 7 for x 0, find lim f(x).

A:

Q: 2. Explain what it means to say lim f(x) does not exist. Again, be sure to explain the concepts!!

A: Given :limx→3fx does not exist

Q: d. lim x_1 x-1

A: Since there are multiple questions so according to guidelines we can solve only first one.

Q: -5 -4 Ef +3 graph below is the function f (x) -3-2 -3) = lim f(x) = -3- f(x) = f(x)= 5 4 3- 2 +…

A: Explanation of the answer is as follows

Q: 4) Let f(x) = x-31, Find (a) lim f(x) x-3+ (b) lim f(x) x-3 (c) lim f(x) X-3 X-3

A:

Q: Let f(x) = x/² for x0. show that lim f(x)=lim f(x)= too X-50+

A: Find the limits with the psoitive and negative values.

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&lt;3   2-x,    if x⩾3 now I am attaching image so that you can easily understand…

Q: Use the graph of the function f shown below to respond to each prompt. The first prompt is worth 3…

A:

Q: 2x 1 if x 2 . Sketch the graph of f(x) = x 4. a) lim f(x) X-2 b) lim f(x) x-2+ c) lim f(x) X-2

A:

Q: Find the following (if they exist) for the function whose graph is given below:

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: Find. 1) a. lim f(x) and b. lim f(x). 3- 4-

A: Answer and explanation is given below..

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…

Q: If f is C2 on an interval prove that f(2 + k) – 2/(2) + {(z =A) = r"(2). - lim h-0 h2 = f"(x). The…

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.