Analyze the following limits and find the vertical asymptotes of f(X) =- x2 - 169 a. lim f(x) x13 b. lim 1(x) lim f(x) C. x-- 13" x- 13* a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. lim f(x) = (Simplify your answer.) OA. x13 B. The limit does not exist and is neither oo nor - oo.

Q: ate the following limits: a) lim(1 – 2x)/x b) lim -) X-0 X0*

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the limit analytically. You must show your work. If the limit doe not exist, be sure to state…

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Q: (а) lim х — 1

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Q: Use l’Hospital’s rule where applicable to find the limit.

A: the given limit is: limx→08x6+3x4-9x9x7-2x4+x3 we have to evaluate the given limit.

Q: Calculate the limit lim |x+2| / (x+2) as x is approaching 5000^-

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Q: Calculate the limit lim 2 / 5x-15 as x goes to 3^+

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Q: Compute the limit below. Justify your answer. 2x2+5x -52 lim- .3 x-4 X°+9x-100

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Q: Q4: Find the following limits if exist:-- x-1 x2-x 1) limx-1²+2x-3 2) limx-1 x²+3-2

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Q: x² – 1 lim x→1 x – 1

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Q: Evaluate the following limits. If you use l'Hospital's Rule, be sure to indicate when you are using…

A: Evaluate limits:

Q: In terms of limits, what does it mean for f to grow faster than g as x→∞? Choose the correct answer…

A: We need to choose correct option.

Q: 3x – x² + 12x – 4 lim - 3x+ – x³ + 3x² + 2x – 1

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Q: Find the limit. lim x→0 x – 1

A: Given that: limx→∞5x-1

Q: Use l'Hôpital's rule to find the limits x- 2 7. lim X2x - 4 x? - 25 8. lim -s x+ 5

A: l'Hospital rule is used when the value of the function is not defined by directly substituting the…

Q: 2. Determine the following limits. If the value is infinite, specify o or - o with enough…

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Q: Find the indicated limit 2x lim( Vx +1 10)

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Q: Find the following limits if they exist. 1. 8.x 4x +1 lim lim 5x-7 Xー→+0 ズー-の 2.

A: Given that limx→∞ 8x5x-7. Compute the limit as follows.

Q: Determine the following limits or state that they do not exist.

A: a. limx→3+2x-33=∞   ∵x-3 tends to 0 from the right side as x tends to 3 from the right side. b.…

Q: Q.4. Calculate the following limits, if exist. 5x4 - 4x3 -x lim 10x3 -6x4 - 2x 1) x2 -16 lim x-4 x2…

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Q: Evaluate the following limits, or explain why the limit does not exist. Be sure to show your work,…

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Q: what is the lim x->0  f(x)-f(0)/x^2 if f(x)=2x^2+1?

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Q: If Lim [x3 – g(x)] = 12 as x tends to 3, use the Rules of Limits to find Lim g(x) as x tends to 3.…

A: Given: limx→3x3-gx=12

Q: Find the limit.

A: The limit of a function limx→Xfx=Y means that the value of function fx can be as close to Y by…

Q: Determine the following limits or state that they do not exist.

A: Given

Q: lim 2 x²-9 2 x² - 4x +3 where c = 0 and 1

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Q: Determine the limit by sketching an appropriate graph. - 5x + 5 for x<4 lim f(x), where f(x) = x-4+…

A: We determine the limit of a function at a given point using the graph.

Q: V x2 + 9 - 5 lim X→-4 x + 4

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Q: a) lim 3x2-10x5

A: Find the limit of 3x^2-10x^5 at - infinity

Q: Find the indicated limit lim(3.x – V9x - x) 2 treat the expression as a fraction whose denominator…

A: To find the limit: limx→∞ 3x-9x2-x=limx→∞ 3x-9x2-x1 Rationalize the numerator first: Multiply…

Q: Evaluate the limits by previous methods or by L'Hospital's Rule, if applicable: a) lim- X- sin x -X…

A: We have to find the limits of the given following conditions

Q: Find the indicated limit 2x lim(- VX +1 X>00

A: This question is related to limits, We will solve it using given information.

Q: Evaluate the following limits if they exist x +5x-3 a) lim x² + 2x – 6 x² – 3x – 1 b) lim x' +1 c)…

A: In the question we have to calculate the limit of the following functions given.

Q: (b) Given that lim f(x)== 2 and lim g(x) =4 , find the limit x→2 x→2 1 lim 3f(x)- Vg(x) x→2 Using…

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Q: Next Evaluate the limit: 2x + 12 lim I+ -6 x2 36 -

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Q: Use l’Hôpital’s rule to find the limits

A: We have to find the limits using L' Hospital's rule: limx→-5x2-25x+5 Since it is 00 form so we can…

Q: Vx +7 lim x-2 x2 – 4x +4

A: Given,            limx→2x+7x2-4x+4

Q: 2) Find the following limits if they exist. a) lim xVx* +1-x lim(x+e')% b)

A: We have to find out limit

Q: Evaluate the following limits and give the equation for any horizontal asymptote (if there are none,…

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Q: Evaluate the following limits: -5x - e* Lim -40 12 sin x i. lim x → 00 ii. x-4,

A: We are given two limits to evaluate.  Both of them are of inderminate forms.

Q: x - 27 a) lim 4x - 3x² - x +3 b) lim x-+3 X-3 X-1 1 1 x+8-2 c) lim d) lim X2 X+2

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Q: A graphing calculator is recommended. For the limit lim (x - 4x + 5) = 20 illustrate the definition…

A: Consider the limit: limx→3x3-4x+5=20  Find the largest possible values of δ corresponding to ε=0.2…

Q: Find the following limits. x²+3x-4 x -16 1. lim 2. lim X-1 X-1 x+2

A: Apply the limit to the given expression and if it results in 0/0 form then take the derivative of…

Q: Find the limit, if it exists. lim ( 4xcosx -95 x2)7 (48x). Round your answer up to 2 decimal places.

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Q: find the indicated limit

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Q: Evaluate the limit lim x² + 4x – Vx² + x ) and interprete the result in relation to x 00…

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Q: What type of discontinuity is at x = 3, if lim f (x)= 0 and lim f (x)= 0? x-3 x>3* What type of…

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Q: 6x lim С. x→-1- \x+1 х+3

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Q: (b) Given that lim f(x) == 2 and lim g(x)=4 , find the limit x2 1 lim 3f(x)- Vg(x) x→2 Using the…

A: Given thatlimx→2f(x) = 2  and limx→2 g(x) =4    and we have to find the value of the limit…

Q: Determine the values of the following limits. lim 2a? 2x + 4 lim %3D む+1 lim I -1 x -1

A: To find the value of the following limits.

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.