We are given the following. 8x2 - 9 lim 9x? + x - 3 We note that as x becomes large, both the numerator and the denominator become large. Therefore, it is not immediately obvious what happens to their ratio. So, we need to do some preliminary algebra. Recall that to evaluate the limit of a rational function at infinity, we first divide both the numerator and the denominator by the highest power of x that occurs in the denominator. Therefore, we should divide the numerator and the denominator by which of the following? Ox O x2

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Q: Evaluate the limit of the given functions. 3x² - 17x+ 20 25x + 36 1. 2. lim x+44x² t³-1 1 lim t-1…

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Q: Please show step by step how to work out all asymptotes for f(x)=3^x-1

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Q: 3. Consider the following rational functions and by inspecting the functions (not using your…

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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

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

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Q: The process by which we determine limits of rational functions applies equally well to ratios…

A: The given limit expression is limx→ -∞ 1-x3x2+7x5.

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A: Given: Qx=4x+2x2-4 We need to show limx→-24x+2x2-4 by ε-δ method

Q: Evaluate lim f(x) and lim f(x) for the rational function. Then give the horizontal asymptote off (if…

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Q: find the limit of rational function (a) as x→0 and (b) as x→ -o. 5x8 – 2x3 + 9 h(x) 3 + x – 4x5

A: [a]limx→∞5x8−2x3+9−4x5+x+3 Therefore, limx→∞5x8−2x3+9−4x5+x+3=∞

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A: Given: Rational function: f(x)=4x-1x+9

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Q: find the limit of rational function (a) as x→00 and (b) as x→ -o. 9x4 + x 2x4 + 5x² – x + 6 h(x)

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A: You may find my method more appealing and easier. Please look into it

Q: 2x-5+4x² lim 3-5x+x²

A: To find: The limit of limx→∞2x-5+4x23-5x+x2. Given: The limit is limx→∞2x-5+4x23-5x+x2. Formula…

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Q: The process by which we determine limits of rational functions applies equally well to ratios…

A: To find the limit  limx→-∞4-3x3x6+9

Q: 1. Find the lim zx*-13x-7 by completing the table of values (round off your answers to at most x-7…

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Q: What is the value if a so that f(x) has a slant asymptote of y = x + 3. x²+ax+5 What is the limit of…

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

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Q: 2. Find the horizontal asymptotes for the following functions, using limits. x²+2x+1 а. f(x) 4x2+x+5

A: Using definition of horizontal asymptote ,

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Q: Show that 13x - 12 can be made as small as desired by taking x close to 4. lim(4x 2 + 2x + 5) = 5x➔0

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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: 3.) +he norizontal, verticie, oblique asymptotes, if Find any for flx) = 3.(x+2)(x-1) (x - 3 )(x+5)

A: Given:           f(x)=3(x+2)(x−1)(x−3)(x+5)

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Q: 3x-2x+1 5. lim x-1 x+1

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Q: Suppose first that a > 2. b) If æ > 2, then |æ – 2| = x-2 FORMATTING: Your answer should not have an…

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Q: Suppose f(6) = - 9 and f'(6) = 9. Find the following. ef (z) – e-9 lim I6 x2 – 9x + 18

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Q: Find the limits below x³ – 3x + 2 (a) lim x2 – x t3 – 3t + 2 (b) lim t-1 t2 – 2

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Q: The graph of a rational function (2а — 3)(4x + 5) f(x) is shown below. (x) (г — 3)(2а — 3) 12 3 12…

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Q: Show that 13x - 12 can be made as small as desired by taking x close to 4. lim(5x + 2) = 17x➔3

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Q: lim (3x2 – 5x + 9) X-4

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Q: Evaluate lim f(x) and lim f(x) for the rational function. Then give the horizontal asymptote of f…

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