Determine the horizontal asymptotes, if any, of: a) f(x)=(x+1)/(x^2+2x+8) b) f(x)=(x^2+x+1)/(x-6) c) f(x)=(2x+1)/(3x-2)

Q: What are the three cases we must consider for finding horizontal/slant asymptotes?

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Q: Use limits to determine the equations for all horizontal asymptotes.

A: Use the limit  y=x2+99x2+1  =x2(1+9x2)x2(9+1x2)  =1+9x29+1x2

Q: If -x2 - x + 1 ≤ g(x) ≤ x2 - x + 1 for all x does not =0. What is the lim x-----> g(x)?

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Q: 2x-5 lim 3-5x+x² I3D

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Q: Find the limit. - 9x lim x+2 x→-2 - 9x lim x+2 x→-2-

A: To evaluate: limx→-2--9xx+2

Q: Show that lim(5x+2)=-18 x-> -4

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Q: 6. Find the limit of lim -3r+2x-6 Xx-4+6x+9 using table

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

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Q: Does lim—>1 exist? Does lim—3 exist? Are they continuous? Discontinuous?

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Q: What is asymptots and how we will solve asymptots?

A: Asymptotes are the lines that curves approaches, as it tends towards infinity. There are different…

Q: find domain and asymptotes of  fx= x^2+x-2 over x^2-2

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Q: Find the inclind asymptotes of the 3-v3

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Q: Determine the limit: 12x - 10| lim %3D 5 - x X5

A: To find  The given limit

Q: Construct an example of a limit problem that requires the use of a multiplication by a conjugate and…

A: Given - construct an example of a limit problem that requires the use of a multiplication by a…

Q: Find the limits in Exercise

A: Find the limits x→-∞lim(2x+(4x2+3x-2))

Q: 2- Determine the equations of all asymptotes for the function f(x)=(2x++13X³-3x²-…

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Q: Find the limit 1² + 2x lim 2-7 x2 - 41 and explain your answer using the continuity property of the…

A: Solving the limit we get,

Q: Find the limit graphically. Show how the Squeeze Theorem can be used to confirm: lim 5-x2. a. Show…

A: WE USED THE SQUEEZE THEOREM IN PART B

Q: Use limits to determine the equations for all horizontal asymptotes. 1- x y = x² + 1

A: To determine: The horizontal asymptote of the given function with the help of limits. Given…

Q: Find horizontal asymptotes by showing limits for x → ∞, x → -∞. Give some argument (numerical or…

A: find limit for

Q: 5. Prove that lim Show your t→-2 t+2 complete solution.

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Q: 2- -2 -2

A: Asymptote : An asymptote is a line that a curve approaches, as it heads towards infinity.   The…

Q: Now we evaluate the numerator at these values, to check if it is also 0. At x = - the numerator is…

A: Given tnat y=x2+68x2-15x-2numarator=x2+6at x=-18, numarator=-182+6=164+6=38564at x=2…

Q: limit of polynomial functions always exists whatever the value being approached by x. TRUE or FALSE

A: Given query is to find the statement is true or false.

Q: How to find  lim 4-x/x+3 while its approaching 3 from the left side.

A: we have to find limit value as x approaches to 3 from left side.

Q: 5. Calculate limit: lim x³+2x²-x-2 x-2 x3+x2-2x

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Q: Both Trapezoidal Rule and Simpson's Rule give the same result when applied to any polynomial of…

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Q: 3) Find the vertical asymptotes (verify with limits) 2 x² - 4 f(x) =

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Q: 2 Find the limit or show that it does not exist. 8. lim (/4x2 + 3x + 2x) X→-0

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Q: 2. Rationalize lim(Vx² +1-x) -1- x

A: We have to find limit

Q: Which statement is true for the limit lim 71-9z+4 I0 5z3+4z2-8 Select the correct answer below: O…

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Q: Find vertical and horiztonal asymptotes for r(x)=8x^3/x^3+2x^2+8x

A: We generate vertical asymptotes  by the zeros of denominator ,so set denominator equal to zero as…

Q: Find the limit. 28x-7x lim x4 x→4 2-x 2. 28x- 7x lim 日 x→4 2- Vx (Type an integer or a simplified…

A: The solution are next step..

Q: Use limits to determine the equations for all vertical asymptote. y=(x2-x-2)/(x2-2x+1)

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Q: Evaluate the limit: lim 1-16 x3-8 x2 limit as x – - > 2 x ^ 4 - 16 divided by x^ 3 8

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Q: In Exercises 55–72, sketch the graph of the function. Indicate the tran- sition points and…

A: y=x+3 is a linear function, so it will not have any transition points or asymptotes We make a table…

Q: What is the end behavior of a polynomial function of degree 7 with leading coefficient -2?

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Q: Create a Piecewise function that:   a) has infinitely many vertical asymptotes and infinitely many…

A: Consider the equation

Q: What are the three different types of asymptotes, and when do they occur?

A: The three types of the asyptotes are: 1. Vertical asymptote 2. Horizontal asymptote 3. Oblique…

Q: The result of the under limit is * 2x+3x lim 5x2-2x+5 O Negative Infinite Value Positive Infinite…

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Q: Explain why a polynomial of degree 3 has at least one root. Start by examining the end-behavior of a…

A: According to the given information, it is required to tell why a polynomial of degree 3 that has at…

Q: Explain why a polynomial of degree 3 has at least one root. Start by examining the end-behavior of a…

A: When a > 0limx→-∞ f(x) →-∞limx→∞ f(x)    →∞ When a < 0limx→-∞ f(x) →∞limx→∞f(x) →-∞ Hence…

Q: that has vertical asymptotes x =-2,x=5 and a horizc

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Q: a) calculate the limit x--> -7 x^2+6x-7/x+7 without using L Hoputals rule    b) calculate lim x-->…

A: Given: calculate

Q: Find an upper limit for the zeros of 2x4 - 7x3 + 4x2 + 7x - 6 = 0 5 4 -1

A: The given polynomial is  2x4-7x3+4x2+7x-6= 0

Q: 7. Evaluate the limit: 9x2 -2 lim 2 3x 2 x-3

A: To evaluate the limit:limx→239x2-22-3x Solution: It is 00 form. We will use L-hospital rule. In…