which of the following statements is true about the function             3x-2, if x<2 r(x)=     -8      if x=-2              5x+4 if x>2 a. f(x) is not continuos because f(-2) is not defined b. f(x) s not continuos at x=-2 because     lim f(x)≠ f(-2)                                                                          x->-2 c. f(x) is not continuous at x=-2 only d. f(x) is not continuos at x=-2 because lim   f(x)      ≠  lim  f(x)                                                                         x->-2-           x->-2+

Q: . Evaluate the following limits and interpret your result in terms of V.A. or H.A. 3-7x a). lim Xo…

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Q: Determine the value for c so that lim f(x) exists. X-4 x2 - 9, for x4 The value of c is

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Q: Let f(x) be given by x²+1 if x 2 Find lim f (x) x-2 (А) 5 B 0 -5 D the limit does not exist

A: As it is the concept of limits. First we will check whether the limit exists or not. We will check…

Q: Consider the following function T² -7x-18 if x -2 Find lim [f(x)]*. I-2-

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Q: Let f(x) = 3x – 4 and g(x) = 8x² + 2x – 2. What is f(x) limx→-1 g(x) O a. -- Оа. O b. 7 4 1 Ос. 8

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Q: Which of the following defines f (5) for f(t) = Va-4? a) 4 lim +5 x- 5 b) Va – 4 – 1 lim I - 5 c) Væ…

A: fx=x-4

Q: find the limit of rational function (a) as x→0 and (b) as x→ -0. x³ + 7x? – 2 g(x) x² – x + 1

A: Given  g(x)=x3+7x2-2x2-x+1

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Q: Determine whether f(x) approaches o or -o as x approaches 5 from the left and from the right. -1…

A: fx=-1x-52=limx→5--1x-52=limh→0-15-h-52=limh→0-1h2=-∞

Q: Consider the following function. 1 f(x) = (x-4)² Determine whether f(x) approaches or - as x…

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Q: Determine the value for c so that lim f(x) exists. X-3 -7, for x3

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Q: 1. For which function below does lim f(x) = -∞? X-2+ 1 f(x) = - x-2 1 f(x) = - (2 – x) x² - 4 a. с.…

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

Q: Given: x + 1, -2 < x < 0 x = 0 0 < x < 2 x = 2 2, f(x) = -x, 0, 2 < x < 4 х — 4, What is the lim…

A: Consider the given function. fx=x+1,          -2&lt;x&lt;02,                x=0-x,…

Q: 3. Given the following piecewise function (x² – 4x – 5, x # -3 13 – x, x = -3 f(x) = Determine the…

A: As per the company guidelines we are supposed to answer only the first three subparts.Kindly repost…

Q: 3 For the following function: f(x)= 2- x a) What type of discontinuity exists at x =2? 3 .? x→2" 2 -…

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Q: For the functionf(x) given below, evaluate lim f(x) and lim f(x). x00 X→ー0 f(x) = -5x - 3x + 2 cos…

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Q: Consider the graph of y=f (x) 5 3 C -5 -4 -3 -2 -1 10 11 -1 Which of the following is true? (A X--3…

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Q: Consider the following function and graph. f(x) = 4 %3D x² - 16 6 -10 -8 -6 4 -2 6. 10 Determine…

A: The given function is, From the above expression.

Q: (4) Consider the function + 3bx + 262 if x 1 For which value(s) of b does lim f(x) exist? Justify…

A: Given: fx=x2+3bx+2b2             if x&lt;1 fx=x-1                             if x≥1 limx→1fx…

Q: 1. If f(x) = x² + 4x – 5 and g(x) = x – 1, then lim f(x) equals x→1 g(x) с. -1/6 а. -6 b. 6 d. 1/6

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Q: If f(x) = 3x2 - 4x +1 and g(x) = x² + 2x - 3, then what is lim 9X, g(x). X-1 f(x)

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Q: If 1/(x^2 + 1) ≤ f(x) ≤ 1 + x^2 for all x in the interval (−1, 1), what is lim x→0 f(x)?

A: Please refer the attached image for complete solution.

Q: Suppose that following is true. x2 + 6 if x s 0 if 0 <x < 1 f(x): 7x² - 6 if x 2 1 What is lim f(x),…

A: Just compute right hand limit and left hand limit and see if they are equal or not.

Q: Is the given function continuous at a=7 ? x2-49 if x=7 f(x)=. x-7 if x=7 Solution: f(a) lim f(x) =…

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Q: 4. What is the sign of a if f(x)= ax' +x +1 satisfies lim f(x) = 0? x→-0

A: Given that fx=ax3+x+1 satisfies limx→-∞fx=∞. Note that the given polynomial having odd degree.

Q: 2. lim (e* +3x)

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Q: 2. Let x+1 r -1 Determine if lim f(x) exists. r-1

A: The objective is to determine if the limit exists or not.

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…

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Q: Calculate the value of the following limits algebraically, (if they exist): 2x²-3x-9 a) lim x-3 x-3…

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Q: Let f(x) = Vx - 1 if x>4 and f(x) = x² – 4x + 1 if x < 4. Find: %3D lim f(x) x→4

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Q: . What is the point discontinuity of the x² – 1 lim x→-1 x +E 1

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Q: Determine the value for c so that lim f(x) exists. x-3 f(x) = 5**, *+c, for x 3

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Q: Determine the value for c so that lim f(x) exists. X-3 f(x) = 3**c, for x3 %3D

A: NOTE: Refresh your page if you can't see any equations. . find the left side limit of the function…

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

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Q: For all x > 0, 4x – 9< f(x) < x² – 4x + 7. Find lim f(x). x→4'

A: As per the policy, we are solving first question only, please  repost and specify which question is…

Q: Determine the value for c so that lim f(x) exists. X-3 f(x) = +c, for x3 The value of c is.

A: Topic = Limits

Q: Determine the value for c so that lim f(x) exists. X→3 1 f(x) = 3*+c, for x3

A: Given that,

Q: It was determined that the lim f(x) = 0 and f(2) = 0. Can it be concluded, definitively, that f'(2)…

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Q: (2) Suppose that a function f(x) is defined for all real values x except x* x,, then lim f(x) does…

A: For limit to be exist at a point, left hand side and right hand side values of function should be…

Q: Given the function f(x) = 4x - x + 4, determine: f(z) – f(x) a) lim Z-X

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Q: Evaluate the left hand and right hand limits of the function defined by (1+x, if 0 1 at x 1. Also…

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Q: Consider the following function and graph. f(x) = 5 x2 9. 2 -10 -8 -6 -4 -2 4 6. 8. 10 -2 retermine…

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Q: * :Test the following function using limits x² - 25 lim x→→5 x² + 2x - 15 B) 5/3 A) 5/4 O C) 5/2 O

A: Apply the following steps to find the value of the given limit. Factorize the expressions in the…

Q: 6. Explain why the limits lim f(x+h) – f(x) and lim f(2) – f(x) h Z-X are each initially in the form…

A: Given that the limits are limh→0fx+h-fxh and limz→xfz-fxz-x.

Q: 10. Use the squeeze theorem to find lim f(x) if 2x+2 ≤ f(x) ≤ x² +3. x-1

A: Given: Use the squeeze theorem to find limx→1f(x) if 2x+2≤f(x)≤x2+3

Q: What conclusion about f(x) can be drawn from the equation lim-a+f(x) = f(a)?

A: Given that limx→a+f(x)=f(a)

Q: Suppose that following is true. (x2 + 5 f(x) = {x (6x² - 5 if x s0 if 0 < x < 1 if x 21 What is lim…

A: To check the existence of function at x = 1 We will calculate LHL and RHL if they are equal them…

Q: Find the limits. f(x) = x + 3 g(x) = x2 (a) lim f(x) X→-1

A: A limit tells us the value that a function approaches as that function's inputs get closer and…

Q: Evaluate the following limits. 2. e* + e-*-2 a) lim b) lim (1 +2x) 3/ 3/x x2 c) lim x2 In x x-0*

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

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.