Prove directly with  definitions that if g : ℝ → [1, ∞) is a function so that limx → c g(x) = L, then limx → c 1/g(x) = 1/L. ii. Prove the same result of the previous part, using Relating Sequences to Functions.

Q: 1 lim x x→0

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Q: 2. Use the ɛ-d definition of the limit of a function to prove that lim = 3. I-»3 T – 2

A: Let  I  be an open interval containing  c , and let  f  be a function defined on  I , except…

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A: Show that:

Q: Prove directly from the definitions that if g : ℝ → [1, ∞) is a function so that limx → c g(x) = L,…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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Q: Prove directly from the definitions that if g : ℝ → [1, ∞) is a function so that limx → cg(x) = L,…

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Q: 5. Determine the infinite limit. a). f(x) = lim +1 x-5 2-t b). ƒ(t) = lim t→1 (t–1)2 x→5-

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Q: Prove directly from the definitions that if g : ℝ → [1, ∞) is a function so that limx → c g(x) = L,…

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Q: 2.x – 7x + 8 Part B: Consider the function f that is defined on R - {2} as: /( x)= x- 2 2 1) Prove…

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Q: a. If f is continuous, then ſ f(x) dx = lim ſ´, f(x) dx. t-00 b. If f(x) < g(x) and g(x) dx…

A: a.) If f is continous then the given condition on the integral is always true. b.) This is a false…

Q: i. Prove directly from the definitions that if g : ℝ → [1, ∞) is a function so that limx → c g(x) =…

A: As directed, solution for the second part is given below.

Q: 1. Let g: DR be a function on D and (c, ∞o) C D for ome ce R. Then lim g(x) = 1 (1 € R) if and only…

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Q: E. i. Prove directly from the definitions that if g : R → [1, ∞) is a function so that limx→ c g(x)…

A: The objective of the question is to prove that if g is a function from R to [1, ∞) such that the…

Q: P) Find T(X) X→-1 f(x) -2 A) -1 C) 0 B) Does not exist D) -2 21

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Q: Suppose that f is a function that is continuous at a number c. Which of the following statements I,…

A: The function f is continuous at a number c.

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Q: 8. Suppose that f is a continuous function with f(x) > 0 for all real numbers x, and lim f(x) = 0 =…

A: Consider the provided question, Suppose that f is a continuous function with f (x)&gt;0 for all real…

Q: Evaluate the limit lim 6 (²1) y→2_8y²(y − 1)³

A: To evaluate the following limit. limy→2 6y2-18y2y-13

Q: 4. Let function g: R → R be defined by g(x) = |x|. g(0+h)-g(0) h B. The value of lim 9(0+ h) − g(0)…

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A: See the solution below.

Q: Suppose that 0 &lt;ƒ′(x) &lt; 1/2 for all x-values. Show that ƒ(-1) &lt; ƒ(1) &lt; 2 + ƒ(-1)

A: From the given inequality the behaviour of the function can be determined as.

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Q: B. i. Prove directly from the definitions that if g : ℝ → [1, ∞) is a function so that limx → c g(x)…

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Q: 3. Consider the function f defined below. Inx for 0<xs2 If f(x)={ then lim f(x) is **]x²In 2 for 2…

A: Given:  fx=lnx         for 0&lt;x≤2x2 ln2     for 2&lt;x≤4limx→2 fx=?