Explain in your own words what is meant by the equation lim f(x) = 5. Is it possible 1. for this statement to be true and yet f(2) = 3? Explain. x→2 %3D Explain in your own words the relationship between infinite limits and vertical 2. asymptotes. Using your answers, evaluate lim and identify any vertical asymptote. x→2

Q: (а) lim х — 1

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Q: If lim f'(x) =0, then the graph of y= f(x) has a horizontal asymptote. %3D Select one: O True O…

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Q: Question 6 Prove, using the formal definition, that lim,→8(x)'/3 = 2. %3D

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Q: Solve the following by definition only: lim (4x - 5) = 7 as x approaches 3.

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Q: For numbers 26-30,consider the graph at the right. 3+ -4 -3-2 -1 1 -2+ -3+ 26.What is the lim f(x)?…

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Q: Determine whether each of the statements that follow is TRUE or FALSE. If a statement is true,…

A: Note that, the Limit of a function f(x) as x approaches c is the value which f(x) approaches as x…

Q: The graph below is the function f(x) 5- -4 -3 2 -1 Find lim →4 Find lim →4+ Find lim H-4 4 30 1 f(x)…

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Q: lim 4x X f(x) ?

A: Using approximate approach ing toward 1/2

Q: From the below graph (figure 1.1.2) the value of lim f(x) = x→-2+ figure 1.1.2 yA 6- -2 0 1 3 f(x),…

A: For the given limit

Q: lim 3x + 1 x-2

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Q: In the below graph (figure 1.1.2), figure 1.1.2 -2 1 3 f(x), lim f(z) Z4+ -3 O 0

A: To find limit f(x) from the graph.

Q: x +7 b. lim x→3 (x - 3)2

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Q: In the below graph (figure 1.1.3), figure 1.1.3 10 -2 3- -4- -s lim f(x) = x-4+ %3D -3 O 6 1 -2

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Q: lim x cscx x→0

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Q: Let graph (x) as below: -6 Solution of lim f(x)is.... x→0* O -2 O 3 O -3 O 2

A: Consider the graph of f(x)

Q: 4. lim e3x+* ,

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Q: (x + 3)² lim – 9 = 3 2x

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Q: 4. Sketch the graph that satisfies the given conditions: fis odd, f' (x) 0 for x > 2; f"(x) > 0 for…

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Q: Find the following limit without using a graphing calculator or making a table. 3x4h - 2xh² lim h→0…

A: topic- limits

Q: Answer the following from the given Graph: 5- 3. -3 -2 -1 1 3 -1 lim f(x) Choose.. 4. 2. 2. 4.

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Q: Complete the following tables of values to investigate lim x→0 x − 1 x + 1 .

A: Consider the function fx=x-1x+1. Compute the value of the function for random values and then make a…

Q: 3) In the below graph (figure 1.1.2), figure 1.1.2 1 3 f(x) New enshot then find the value of the…

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Q: 1,0 1.0 10 -6

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Q: Without a table of values and without graphing f(x), give the values of the following limits. lim 3x…

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Q: 2x 9. x-1 lim x-3 6-2x

A: Given limx→32xx-1-9x6-2x

Q: Find the limit. (7 +2) 8 lim X→ 00

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Q: lim f(x) = 3 lim f(x) = x→2+

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Q: Given a function whose graph is shown below. 14 3 2. 1 -6 -3 -2 1 3 4 5 6 7 8 -3+ -4 What is lim f…

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Q: Please find the limit (in terms of the constant a).

A: it is given that

Q: Question 3: Evaluate the following limits, if they exist, by using the graph -5 -4 -3 -2 -1 3 -1 -2…

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Q: |x – 2| 27. lim x-2 X – 2

A: Given data: The given limit of the function is limx→2x-2x-2. The expression for the left-hand limit…

Q: Use the graph to answer these questions a Find lim 1(x) and lim 1(x). x-4 b. Find lim f(x) c Find…

A: a) limx→4+f(x)  is the value that the function approaches to from the right sideFrom graph f(x)…

Q: Answer the following: Show your solution below: a.      Use graphing platform to graph the function…

A: Given,        limx→1-x2+x+1x3-1=

Q: From the following graph, the value of lim f(x) is 0.5 -5 -3 -2 1 2 f -0.5- -1.5- -2

A: Hair we have to find out the limit approaches to x = 2.

Q: In the below graph (figure 1.1.3), figure 1.1.3 10 -2 4 -1 -2 -3 lim f(x) = x→-4+ in

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

Q: Complete the following table to evaluate the limit lim Step lim x+√x Step 1 Step 2 Step 3 Step 4…

A: The answers for each step are as follows.

Q: From the graph determine lim (x) *-2* O 1) 1 O 2) 2 O 3) 3

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Q: Given the graph of the function below, what is lim f(x)?

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Q: Given the graph of f(x) below, what is the value of c such that lim, se (z) - f(c)? O b. 1 OC -5 Od…

A: We have to find where Left Hand Limit= Right Hand Limit= function value

Q: According to the graph of fx) given below, f(x) – 2 (a) Is lim positive? ("yes" or "no") [a] x+0 (b)…

A: According to our guidelines, we can answer only the first question, the rest can be reposted.

Q: If f (a) = 3, then if lim f(r) exists, it equals 3. %3D For those who have trouble viewing the…

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Q: 1. Complete the following tables of values to investigate lim,-1(x2 – 2x + 4) f(x) X 0.5 0.7 0.95…

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Q: x+3 lim x+6x+9 X-3

A: Given, limx→-3x+3x2 +6x+9   We have to find the value of  above limit

Q: From the following graph, the value of lim f(2) is I-3 1- 0.5 -5 -4 -3 -2 -0.5- -1 -1.5 -2 L L... L

A: From the given graph

Q: Use the graph of the function ?=?(?)to find the given values, if possible. Estimate when necessary.…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: S Student: Sect Instructor: Solve the following problems: 1. Sketch the graph and evaluate the lim…

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Q: From the graph given below, the value lim, 6- f(x) is Are 1.1.3 2 4 -1 .. -4- O a. 0 O b. 5 O c. 1 O…

A: The solution is as follows:

Q: From the following graph, the value of lim f(x) is

A: The graph of f(x)

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: