Evaluate lim f(x) and – o where appropriate. Then give the lim f(x) for the following rational function. Use oo or X00 X - 00 horizontal asymptote of f (if any).. 12x-8x+ 7 f(x) = %3D 4x +1

Q: х3-2х-1 lim x-3

A: This question is based on Limits

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A: Explanation of the answer is as follows

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A: Given: limx→32x2+5x-33x2-9

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Q: [0] lim 0→3+ 0

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Q: Calculate the limit algebraically. (If an answer does not exist, enter DNE.) lim x→1 (4x − 10)

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Q: If Зx <f(x) < х +2 for 0 <x< 2, find lim f(x). х—1

A: Result used:

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Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (V 9x² + x - 3x) X- 00

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Q: Evaluate lim f(x) and lim f(x) for the following rational function. Use co or - 00 where…

A: Note: In the first question, you have not uploaded the question with the options. So solved the…

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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=-∞

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A: WE have to use the graph of f(x)=ln(x) to find , a) limx→0+f(x) b) where does the function ln x have…

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A: Given x≥2,the horizontal line y=2 is an asymptote

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A: Part (a) - Let the given limit be y - y = limx→-1 3x-5Putting limit x=-1, because we do not have any…

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Q: Determine lim f(x) and lim f(x) for the following function. Then give the horizontal asymptotes of f…

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Q: 4x23x 4х — 1 5 Find lim f(x) if x2 х> со

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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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Q: Use lim f(a+h) - (f(a)/h to find f(a) at given number a. f(x)=4x6 a=-1 so far I got to: 4 (-1 + h…

A: To find by using derivative definition

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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 ,

Q: Find the value of Vx+3-/3 lim lim,-5* |x-5|(x²+5) (x-5) 1 O -20 2+/3 O 130 O none О 30 2 V3 O None 1…

A: 1) find the value of limx→0x+3-3x rationalize the numerator limx→0x+3-3x=limx→0x+3-3x×x+3+3x+3+3…

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Q: 4. Use the following function, f(x), to find lim f(x). Remember to show your work. 3x² – 4 x 2

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Q: Find the following function, state the following: f(x)= (2x^3-8)/(x^2+2x-8) x intercept: y…

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Q: X-9 lim

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Q: Given f(x) = 4 – a² and g(x) = væ + 1, find lim g(f(x) 2

A: Given,     f(x)=4-x2        and     g(x)= x+1then, to find                 limx→1gf(x)=?

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Q: a. For the function graphed here, show that lim,-1 8(x) # 2. b. Does lim,-1 g(x) appear to exist? If…

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

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Q: -x2 if x 3 Iff (x)

A: Take value of f(x) for value of x just less than zero.

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Q: Find lim f(x) for the given piecewise function. 2x +3 f(x) = { 5 -*+18 if x > 6 if x < 6 %3D if x =…

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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…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: