Suppose that f (x), g(x), and h (x) are defined for all æ # a over an open interval containing a . Suppose that: f (x) < g (x)

Q: If f(x) is defined by the following ²-16 =x2-4 2-3x-1 Let f(x) x> 2 *<2 Then find the lim f(x) & lim…

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Q: Determine the limit and exact value of each function given c. 1) f(x) = x² – 2x + 4 f(1) = lim x² –…

A: Given,f(x)=x2-2x+4 Substituting,x=1 in f(x) we get f(1)…

Q: 1. Let f(x) = 3² – 2x + 1. Compute lim (x)f – (4 + x)f 0+-4

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Q: 5. Evaluate each expression using the given graph of f(x). lim f(x) a) x-1- 2- 1- b) lim f(x) -2 -1…

A: Given graph, The objective is to find,  a) limx→1-f(x)  b) limx→1+f(x)  c) limx→1f(x) d) f1 e)…

Q: (4) Let f(x) be the function whose domain is all of R given by the rule 42 if r € Z and f(x) = 10…

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Q: Use the graph of f(x) below to answer the following questions: -1₁ --2 y=f(x) 3₁ 4₁ I 5 I I X

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Q: Suppose f: (0, ∞o) → (0, ∞o) is a continuous function. True or false: lim √f(x) = = /lim f(x). 2-5…

A: We have to find whether given statement is true or not?

Q: , if x + -1 -2, if x = -1 Prove that f(x) = {x+1 is continuous at a = -1 by showing the following.…

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Q: which of the following statements is true about the function             3x-2, if x&lt;2 r(x)=…

A: We have given,            3x-2, if x&lt;2r(x)=     -8      if x=-2             5x+4 if x&gt;2

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: If a function f(x) is given by x²-2x-8 T²-7x+12' 6, is f(x) continuous at x = 4? = x 4, x = 4, Yes…

A: The given function fx=x2-2x-8x2-7x+12,x≠46,x=4. We have to check whether the function is continuous…

Q: Suppose f(x) has a removable discontinuity at x=10. How do we redefine the function to make it…

A: This question can be solved using the concept of limit and continuity.

Q: Show that if lim f(x) = lim h(x) = 3, and if f(x) ≤ g(x) ≤h(x) for 2-0 x-0 all z € (-1,1), then lim…

A: Given that limx→0fx=limx→0hx=3 and fx≤gx≤hx for all x∈−1,1. We have to prove that limx→0gx=3.…

Q: For real number p, let f and g be defined by f(x) =er³ and g(x) =1/xP, respectively, on [1,00). f(x)…

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

A: Above question is solved.

Q: suppose f,g an d h are functions which g(x)<=f(x) <=h(x) ,for all x in an open interval containing a…

A: No. For the given continuous open interval domain, the limit of f(x) does not exist.

Q: Given f(x) = x² + Va, then f(4+ h) – f(4) - a) lim h>0 h f(æ) – f(1) x – 1 b) lim Note: write either…

A: This question can be solved using the concept of function and rationalization.

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: If f(x) = 2x? – x + 2 , what is lim 2x2 – x + 2, lim 2x2 – x + 2, andf(2)? Is f(x)continuous at 2? O…

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