Use the function and graph to answer the questions about existence, limits, and continuity. -x-3, - 5sx< - 4 x+5, - 4

Q: Solve for the limits of the following functions. Show complete solution.

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Q: Use properties of limits and algebraic methods to find the limit, if it exists. x+13x+42 lim x +6x…

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Q: (a) Estimate the value of lim x→ - infinity square root x^2+x+1   +1 by graphing the function…

A: Solution(a)To evaluate:  limx→∞ x2+x+1 + 1 by graphing the function------------------------fx…

Q: 13. Find the limits algebraically lim 5x+2 2х-3 x→3 lim (-x' + 10x? – 33x + 38) x→3

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Q: f(t) = 3 – 9 ? -6, [-3, 3]

A: To find: The continuity of the function f(t)=3-9-t2 on the interval [-3, 3]

Q: Find lim x→-∞ ex + 1° (а) — оо (b) ∞ (c) 0 1 (d) 2 Does not exist and has no infinite behavior

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Q: V5x+9-3 -lim x+0

A: To evaluate: limx→05x+9-3x which is in 00 form. So, the L'Hopital rule is to apply.

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: 2, if x -1 Find the value for a and b such that f (x) = {ax + b, if – 1 3 for all real numbers.

A: NOTE: Refresh your page if you can't see any equations. . the function is continuous at x=-1 so we…

Q: What is the limit as x approaches -2 from the left? 3 1 -1 2 r = 2 -1 -2 +00 -2 - 00

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Q: x²+1 lim x-5 √2x+2-2

A: We have to evaluate the limit.

Q: Evaluate the limit of x approches 0 on the function (2e^(9x)-2)/(7x)

A: The given limit of the function to be evaluated is,

Q: 3x -10x+7x-12 7. lim x--1 x-2

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Q: Graph the function (1 x<-1 -x -1<x< 0 f(x) = {1 x = 0 0 <x <1 1 x 21 Then discuss, in detail,…

A: Given: f(x)=1,x≤-1-x,-1&lt;x&lt;01,x=0-x,0&lt;x&lt;11,x≥1 To Discuss: Limits, one-sided limits,…

Q: find the limit of rational function (a) as x→00 and (b) as x→ -o. 3x7 + 5x? – 1 f(x) 6x3 7x + 3 -

A: (a) Given f(x)=3x7+5x2-16x3-7x+3 For x→∞…

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: Graph the function 1, x <-1 -1 < x < 0 -x, x = 0 f(x) = 1, 0 < x < 1 x 2 1. -x, 1, Then discuss, in…

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Q: either evaluate or explain why limit does not existlim f(x) x --&gt;5 where f(x) {x+3, if x does not…

A: We'll answer the first question. Since the question is not specified, please submit a new question ,…

Q: Prove the limit statements Sx², X = -2 **-2 lim f(x) = 4 if f(x) I-2

A: Given, fx=x2x≠-21x=2 To prove: limx→-2f(x)=4

Q: What is the limit when x is approaching negative infinity when the function is (8x+2) / (4x-5)

A: Given

Q: Find the limit of the funclion, f, as x approachts 5. f(x)= x?-3x -10 %3D X-5 iMx>s f(x)%3D

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Q: Answer all the following questions 1. Find the domain of f(x) =x-4 x-4 2.Solve the inequality and…

A: 1)domain [−2,2]∪(4,∞)

Q: 6. a) State why the limit of f(x) = √5x - 1 does not exist for x

A: Please refer to the image below

Q: Discuss the continuity of the function on the closed interval.

A: Given:

Q: the limit definition to find the slope of the tangent line to the graph of f at the given point.…

A: Given query is to find the slope of the tangent.

Q: Find the limit if it exists. 5 y = G(x) 4 -2 -1 0 1 2 3 4 | 3.

A: Please refer the attached image for complete solution.

Q: find the limit of x^2/1-4x^2 as x approaches infinity

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Q: Complete the table and use the results to find the indicated limit. x3 If k(x) = 46x - 144 find lim…

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Q: - 3x +4 lim -2 x - 3x + 7x - 24x + 28 a. where a is some fixed real number x = a' b. lim 2x

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Q: Determine whetherthe limit exìsts or not when a) xーヤ 3 and 6) x→-3 F(x) = 1 Vx?4 Wien x<-ろ Vg-x²…

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Q: Find the following limits or state that they do not exist. Assume a, b, c, and k are fixed real…

A: To evaluate limit limx→110x-9-1x-1 This is 00 form. We will use L-hospital rule. In L-hospital rule…

Q: Determine if lim f(x) exists. Is the function continuous at x = 2? Show all the steps. f (x) = { 4 S…

A: Given that a function and we check that at x= 2 this function is continous or not . We know that if…

Q: If the limit of g(x) as x approaches 2 is equal to 7, then g(2) must equal 7.

A: Given data:     The given function is: g(x).     The expression for the limits of the given function…

Q: Use the definition of continuity, along with the One- sided continuity theorem, to determine whether…

A: We first find left and right hand limit at x=4If left hand limit=f(4)=right hand limit, then the…

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) =…

A: we have to find the intervals on which f(x) is increasing and the intervals on which f(x) is…

Q: 3- x, 3. f(x) = [-1,4] 3+x, x > 0 1 4. g(x) [-1, 2] .2 - 4

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

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Q: lyfical of the itemrs need to be factored or rationalied for the limits to exist) - 1. lim (x - 2r)…

A: given,        3.  limx→-4x+42x2-164.  limx→-33x2+2x-1x2+3x+2

Q: Use a table of values to evaluate the limits of the given function

A: Let's find.

Q: a. Determine the value of b to make f(x) continuous at x = -3. Explain your reasoning using limits.…

A: For the function to be continuous value of left limit and right limit should be equal.

Q: 3. lim (4x2 – 3x + 3) x--1

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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: Find the limit of f(x) = 9x+9/8x+8     as x approaches infinity and as x approaches negative…

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Q: Decide if the inequality 4x – 5 < f(x) < x² provides sufficient information to determine the limit…

A: NO, the inequality doesn’t provide sufficient information.

Q: Use limit definition to find f'(2) for the function, f(x) = 3x? – 4x + 1-

A: fx=3x2-4x+1 substitute x+h for x fx+h=3x+h2-4x+h+1 fx+h=3x2+2xh+h2-4x-4h+1 fx+h=3x2+6xh+3h2-4x-4h+1…

Q: Find absolute extrmum(if any) f(x)=x2-4x+5 on [-2,3]

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Q: Question -4xª –8x³ –4x 2 What is the limit as x → +o of f(x) = -3x5+2x² –3

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Q: compute the limits to graph the functionP(x) =x^2−6x^1/3 on the interval [0,4]. Note that P(4) =…

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Q: Find the limit of f(x) = 4x+8/7x+3 as x approaches infinity and as x approaches negative infinity.

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Q: Find all values c such that lim x-2 2c²x 5c +1 x²-3x + 2 - exists. (a real number)

A: We say a limit exists if right hand limit and left hand limits are same. We have…