17. Using the definition you gave in Exercise 2.1.14, show that (a) lim (1-2)=1 2|x| x→→∞ 1 + x (c) lim sin x does not exist X→-∞ (b) lim = -2

Q: f(r) where f(r) and g(r) are polynomials. g(r)' 2. Describe a strategy for solving limits of the…

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Q: Let f(x) = 2/(2 – x) and g(x) = 8/(4 – x²) Find lim [f(x) –- g(x)] 7. a.

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Q: 5. Sketch the graph of one function y = f(x) that satisfies all of the requir- ments below. lim f(x)…

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Q: Answer the following questions. Record your answers on the line provided. 1. Use the graph of y=h(x)…

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Q: n each part below, give an example of a function which satisfies the given criteria. Justify that…

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Q: 3) If the lim f(x) = 2 and lim f(x) = -1 %3D x-3- x-3+ Then what is the lim f (x) = x→3 %3D a) Why?

A: To find the limit of the f(x) at x=3

Q: . Let (x2 + 1 f(x) = 1( - 2)² if x> 1 if x<1 (a) Find lim,-I- f(x) and lim,→* f(x). (b) Does lim ,1…

A: Given: For (a),     limx→1- f(x)=limx→1 x2+1=12+1=2 and     limx→1+ f(x)=limx→1 x-22=(-1)2 =1

Q: If lim f(x) = 5; lim g(x) = 7 then || x4 lim[xf(x)+ 7g(x)) 69 63 O 17 O 149 -29

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Q: 7. Identify if the statement is Always True, Sometimes True or Never True. If lim f(x) exists, then…

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Q: If lim f(x)=-2 and lim g(x) = 2, what is the value of lim [f (x)+2g(x)]?

A: Given, limx→afx=-2  and  limx→agx=2

Q: I if X > 4 and J (X). 4X + 1 i1 X<4. Find lim f(x) x→4+

A: Given; f(x)=√x-1 if x&gt;4 and f(x)=x2-4x+1 if x&lt;4.

Q: b) Evaluate lim g(x) if 2x − 1 ≤ g(x) ≤ x² − 2x + 3 x→2

A: Above question is solved.

Q: b) Let f(x) = x²-1 2-1 ' √x-1 0 < x < 1 1<x<3 2-1 ' 5x+3, 3x Find lim, 1 f(x). 3x-7 c) Let f(x) =…

A: The b part of the question can be solved using the concept of limits.The c part of the question can…

Q: 5. lim x →0- Prove directly from the appropriate limit definition that if lim f(x) = 2,then f(1 x) =…

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Q: Expand the function p (z + h) as follows. p (z + h) = V(w+h)²–1 Substitute the function p (z + h) in…

A: They are solving derivative for v=1w2-1

Q: Let f(x) = x² - 4x-21 X-7 Find a) lim f(x), b) lim f(x), and c) lim f(x). X→7 X-0 X→-3

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Q: 1 (B). Evaluate lim (3 – x) x-2 x→2

A: Given that  lim x to 2 (3-x)^(1/(x-2))

Q: Use the limit definition of the derivative to determine f '(2) if gnibnoqonos su snimals (T ni 4 =…

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Q: 10.   calculate:

A: Step 1: Step 2: Step 3: Step 4:

Q: Graph y = 4x - 3. %3D

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Q: 5. Calculate lim f(x), where x+1+ f(x) = = its 12.05 (c)-2 (d) 2 (e) does not exist 5A 5B if x 1 x-1…

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Q: (a) Lim X–1 x +1 -2 X

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: 3. Sketch a graph of a function (x) for w ich all of the fo lowing are true: lim-2' f(x) = -4,…

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Q: 4. Use the given information to sketch the graph of the function f. (-2,1)u(1,x) all real except X -…

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Q: Sketch a graph of a function that satisfies all of the following properties. -4- a) f(-6) is…

A: We need to sketch the graph.