Let f be defined by:                1,   x rational f(x)={                0,   x irrational ;prove that for no number c does limx->c f(x) exist

Q: 1. Let f(x)= x²+x-6 |x2| 7 x b 2 x + a 3 2 if x 2

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Q: Q:Discuss the continuity of the function f(x) =lim+ sinTt x)" - 1 n- (1+ sinTt x)" +1 at the point x…

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Q: Recall that Q denotes the set of rational numbers. Show that there does not exist a strictly…

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Q: 2. Use the graph of f(x) below to a) determine the domain and range of the function and b) evaluate…

A: This question is related to Functions, we will solve it using given information.

Q: Let f be defined in an open interval that contains a=3 and assume that all x,…

A: f be defined in an open interval that contains a=3 and assume that all x,2x+6≤f(x)≤x2-4x+15

Q: t g(x) = 2x² + 6x – 4 in the interval [-1,1]. Use the Intermediate Value Theorem to determine if a…

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Q: x² -9 f (x) = is 0<x<5 and x=33 at the point 3 x² – 2x – 3° - 1.5

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Q: Suppose that 3- 8x² ≤ g(x) ≤ 3 cos x for all real numbers x. Evaluate: lim g(x) = x-0

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Q: f(x) = x² 8 x + 2 x - 6

A: f(x)=x+2x2−x−6

Q: limx→00 x3 lim,- is x.

A: Limits

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

A: Above question is solved.

Q: Let f(x) = |x − 2| − 1. i) Make a table of ordered pairs for f(x), for all integers x with −3 ≤ x…

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Q: et f(x) xeX. Use calculus to find all the x-values at which f has an inflection point. %3D

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Q: Find lim f(x) if x →∞ 4x - 1 X f(x) 5.

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Q: х — 5, for a 3.

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Q: Use the Squeeze Theorem to show that lim x2 co X-0 cos(207TX) = 0. Illustrate by graphing the…

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Q: 5. Let a, b, and c be real numbers with a < c< b and let f : (a, b) → R be a monotone function. If c…

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Q: Assume that g(x) is a function given by 2.x? + 3x +2 g(x) = x² + 2 Prove that g(x) is bounded for…

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