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A: The solution is given in the next step.
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Q: 3.
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A: Let's find.
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A: We can find the answer as below in simplified form.
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A: Given problem:-
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A: We can solve the limit as below
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A: The objective is to Identify the quadric surface and sketch it's graph.
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A: As you have asked multiple questions so I have answered first question as per the guidelines.
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A: Topic = Functions
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- If x4 <=ƒ(x)<= x2 for x in [-1, 1] and x2<=ƒ(x) <= x4 for x <-1 and x> 1, at what points c do you automatically know limx-->c ƒ(x)? What can you say about the value of the limit at these points?The limit of the function f as x approaches a is the number L, written as limx→af(x) = L, if for every ε > 0, there exists δ > 0, such that if 0 < | x - a | < δ, then | f(x) - L | < ε. Using this definition, prove that limx→1+ 4 / (1-x) = -∞.If 2 - x2 <=g(x)<= 2 cos x for all x, find lim x-->0 g(x).
- Consider the function f(x) = 1/x for x ∈ ℝ and 3 < x < 7. Prove that limx→5 f(x) = 1/5, using delta, epsilon definitionFind formulas for f and g such that limx→∞f (x)/g(x) is an ∞/∞ form that has a limit of ∞.For any real number r, it can be shown that lim x--> ∞ x^r/e^x = 0. Using this fact what is lim x--> ∞ e^x + x^2023/e^2x + x^2
- Consider the limit limx→0 1 x 2 = ∞ and let M = 1000. Find the largest value of δ > 0 such that if x ∈ (c − δ, c) ∪ (c, c + δ), then f(x) ∈ (1000,∞). That is, now close does x have to be to 0 so that 1/x2 is in the interval (1000,∞).Find the limit for lim x -> 0 for cos(1/x)Suppose that lim as x approaches infinity of f(x) + x^2 = L for some number L. Then lim as x approaches infinity of f(x)/1+x-x^2 is?
- Determine value for c so that lim f(x) x--> 3 exists f(x)= 1/3x+c For x<3 -x+8 For x>3a. Graph h(x) = x2 cos (1/x3) to estimate limx-->0 h(x), zooming in on the origin as necessary. b. Confirm your estimate in part (a) with a proof.Find the constant c so that the limit limx->3 (x2+x+c)/(x2-5x+6) exists.