6. Below is the graph of f (x). For each of the given points determine the value of f (a) and lim f (x). If any of the quantities do not exist clearly explain why. (a) a = -2 (b) a =-1 (c) a = 1 (d) a = 3 6 2 1 -3 -2 -1 1 3 -3 -5 4. en 2)

Q: 1. Use your knowledge of graphs of functions and their derivatives to find the value of lim Show…

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Q: 2. Construct a table of values to investigate 1 if x -1

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Q: 11. If f(x)=Vx f(x)-f(4)| The lim x→4 х-4

A: Given: fx=x To Find:  limx→4fx-f4x-4=?

Q: 2. By drawing a graph illustrate an example of a function f(x) such that it satisfies these three…

A: Topic = Functions

Q: What conclusion can be made if: a. A function changes from a decreasing interval to an increasing…

A: Given that: a. A function changes from a decreasing interval to an increasing interval.b.…

Q: Consider the graph of y = f(x). 4- -8 -7 -6 -5 -4 -3 -2 -1O 2 3 5 -2 For infinite limits, use 00 = 0…

A: As per our guidelines we are supposed to answer only first three parts. kindly repost others part as…

Q: Determine whether the shown statement makes sense or does not make sense, and explain your…

A: The functions whose graphs can be drawn without lifting the pencil off the paper is a continuous…

Q: show that : Lim h→0  h / √5h + 4 − 2 =4/5

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Q: 3. Evaluate this limit. x + 4 lim x--4 4x + 16

A: given,

Q: 1.Can you easily apply the addition rule for limits to this function? Why or why not? What is the…

A: As per our guideline we are supposed to answer only one question you can repost other questions in…

Q: Draw a graph where lim x→2 f(x) exists but f(x) is discontinuous at x = 2. Name the type of…

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Q: Determine whether the statement makes sense or does not make sense, and explain your reasoning.

A: Let us consider limx→a-f(x)=A and limx→a+f(x)=B We have, A is not equal to B. When x gets close to…

Q: lim 극 et – 1 x-1

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Q: 5. Sketch the graph of a function f(x) that satisfies the following conditions: lim, - -o f(x) = 00…

A: We can sketch such graphs keeping in mind the graphs of parabola, straight lines.

Q: 4 (a) Evaluate lim,1 (금-) (b) Let f(z) = -r. Find the value(s) of z if the second derivative f"(x)…

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Q: b. f(3) = 2 and lim f (x) does not exist.

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Q: In parts (A)-(C), find the indicated quantity for y = f(x) = 5 – x². A) f(- 1)– f(– 2) (-1)-(-2) f(…

A: Given function is y=f(x)=5-x2f(-1)=5-(-1)2=5-1=4f(-2)=5-(-2)2=5-4=1f(-2+h)=5-(-2+h)2=1+4h-h2…

Q: Suppose a function f satisfies f(3+h) – 2 lim = 7. Find an equation for the line tangent to the…

A: Let

Q: 1. Consider the function f(x, y) = 2y (a) Show that lim (x,y)(0,0) f(x, y) does not exist by using…

A: Note: if a limit exists at a point,it must be the same limit along any path approaching that point.…

Q: Use calculator to tabulate to four decimal places values of 2x2 + 3x – 2 f(x): x2 – 6x – 16 x is –3,…

A:

Q: 3. If f is a continuous function, what can you say about lim f(x)?

A: Given thatf is continuous To determinelimx→1f(x)

Q: Suppose a state's income tax code states that tax liability is 18% on the first $19,500 of taxable…

A: The tax function,   T(x)=a+0.18xx≤19,500b+0.14x-19,500x>19,500

Q: Q1/ Find the following 1. lim x2 + 1 = 2 x00 (x-2)2 2. lim x-2 (x-2)(x+2) 3. lim (5 -) x-0

A:

Q: 1. By using the following graph calculate the following values: y 20 15 10 f (x) 5 -10 -5 -1| 1 10…

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

Q: 13. Sketch the graph of f (x) = }" Sx² + 1 if x -1 and use it to evaluate lim_ ƒ (x) and X→-1- lim…

A: Given that: f(x)=x2+1    if    x≤-13            if     x>-1

Q: 14. (a) Use a graph of 1(6) = (1- 2)" f(x) = to estimate the value of lim f (x) correct to two…

A:

Q: 9. What conclusion can be made if: a. A function changes from a decreasing interval to an increasing…

A:

Q: 2. Create a graph that satisfies the given conditions. im f (x) = -∞, lim f(x) = ∞, lim f(x) = 0,…

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Q: Determine whether the statement makes sense or does not make sense, and explain your reasoning.

A: lim x→4fx = 0lim x→4gx = 0To verify:          lim x→4fxgx ≠ 0   is correct or not.

Q: 3. If f (x) = (x² – 1, if x 3 3.a) lim f(x) X-3 3.b) lim f (x) 3.c) lim f (x) X-1

A: The given function is f(x)=x2-1,if x<3x+5,if x≥3

Q: 4 Use the following graph of f(x). 2- a. find the limƒ (x) x--3 b. find the lim f (x) -2- c. is f(x)…

A:

Q: -2 0 1| 3 What is the 6 5 4 3 2 1 0 -1 -2 -6 lim f(x) for the following graph? X→-3 -5 -4 -3 -2 -1 0…

A:

Q: Find the limits as x - 0o and as x - -00. y = f(x) = (3 – x)(1 + x)?(1 – x)4 lim f(x) = lim f(x) = X…

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Q: Show that the function given below is continuous. 4v2 - 16v lim -2 v-4

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Q: Suppose that f(x) = 2cos (n/3 x) and the graph of g(x) is given by: y = g(x) 2 1 -5 -4 i ż 3 4 5 x…

A:

Q: 1. By using the following graph calculate the following values: 20 15 10 f (x) +++ -10 ++ -5 1 5 10…

A: The figure is given by

Q: (3х + 3с if x >2 Let f(x) = {x2 - cx if x < 2 If lim f (x) exists, find the value of c. X-2

A: Limit of a function exist , when both sided LHL and RHL exist.

Q: 2 3 The graph of the function f is above. At what x= a value(s) in the interval (-2, 5) does a. lim…

A:

Q: 2. Find the following limits. Do (a) and (b) without a calculator and (c) and (d) with a calculator…

A: We have limx→0x-4x+4=limx→0x-4limx→0x+4=0-44=-42=-2

Q: Q.4: Prove or disprove, lim f(x) = 4 If f (x) = } x # 2 x = 2 x→2 2.

A:

Q: 10- In parts (A)-(C), find the indicated quantity for y = f(x) = 5- x. f( - 1)- f(- 2) (A) (-1)-(-2)…

A: Given the function simple put the value of (-1) and (-2)  find the value of y and put it on that…

Q: 3. If f and are continuous functions with f(3) 4 and lim 2f(x)-9(r)3D5, what is g(3)?

A: To evaluate the value of the function

Q: 4. Sketch a graph with the following sets of properties. 10 8 f(5) = 3 f(-1) = -3 4 lim f(x) = 2 2…

A:

Q: 8. If f (x) = -x² + x, which expression represents f'(x) ? -(x+h)²+(x+h)-(-x²+x) А. h…

A:

Q: If f (x) = -x² + x, which expression represents f'(x) ? %3D -(x+h)?+(x+h)-(-x²+x) А. h…

A: We know that f'(x)=limh→0f(x+h)-f(x)h. Here, f(x)=-x2+x.

Q: 2. a. Draw a graph with the following characteristics: lim f(x) = 3 X->2* lim f(x) = 0 %3D x-→2 f(2)…

A: The graph has the properties,limx→2+f(x)=3limx→2-f(x)=0f(2)=3limx→-1f(x)=-2f(-1)=1

Q: ,if x> -3 Given the function f(x) =' 3 ,ifx S-3 is continuous at x=-3

A: A function                      fx=x2-9x+3,   if x&lt;-33,             if x≤-3 We have to answer the…

Q: 1. lim (3x + 4)

A:

Q: The graph of f(x) passes through the point (4, 0). The slope of the line tangent to the graph at 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.