11) In Problems 11 and 12, given f(x) and g(x ) are continuous everywhere with the values: 2 X = f(x) = | g(x) = | 2 1 -1I6 fo l -3 Find lim [g( f(x))] = A) 2 B) 6 C) -1 D) - 3 12) Find lim g [f(x)+ 3]=_ A) 0 B) -1 C) 2 D) - 3

Q: Let f(x) = 1²-16 +4 1²-16 H-4 x > 0 I≤0 Find lim f(1)

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Q: III. Suppose that a function f(x) satisfies the following properties, together with the table of…

A: Given: Properties of a function f(x) are given below, To find: Relative maximum points, relative…

Q: 1. Complete the following based on the graph of f(x). -10-8-6-4-2 81 6 4 2 -21 $ 66 -8 f(x) 2 4 6 8…

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Q: 2. Construct a table of values to investigate 1 if x -1

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Q: 30. (а) f(-2) (b) lim f(x) 4 3+ (c) f(0) 2- (d) lim f(x) (e) f(2) -2 1 1 2 3 4 5 (f) lim f() -2- (g)…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: If f(x) = lim (1+x)(1+x²) (1 + x² ) (1 + x² ).......((1+x) where [x] < 1, then - 618 1 (B) 3) (C)…

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Q: 3. Sketch the graph of a function y(x) with domain (-x, 0) that appears to satisfy each of the…

A: Given: The domain of the function is all real number,  limx→∞y(x)=5limx→-3y(x)=-∞limx→4y(x) does not…

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: 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: fOo)=Sinx-41 Cos x 1X-1 cos X (x)

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Q: lim h(x)= a) x→-1 h(3) = b)

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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: 8. The function g(x) is written as: 5x + 3 if x 1 Find lim g(1+x²) x-0 g(x)= =

A: To find the limit of g(1+x^2) as x approaches to 0.

Q: 3. For each of the following, give an example of a function f satisfying the giver such a function…

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Q: III. Suppose that a function f(x) satisfies the following properties, together with the table of…

A: An asymptote of a curve is a line such that the distance between the curve and the line approaches…

Q: Suppose we know that y x ER, h(x) ç f(x)Eglx) where Determine lim flxl. X -)0 h(x)= 31-4x2 and 9(x)…

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Q: lim f(x) = 2 lim g(x) = 3 %3D 4. Suppose that and then x→1 g(x) – 4 f (x) lim find the value of…

A: Given that: limx→1f(x)=2   and limx→1g(x)=3

Q: 2.) If x= 3, lim In(x+h)-In(x)

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Q: 52. Let X if x 2 (a) Evaluate each of the following, if it exists. (i) lim g(x) (ii) lim g(x) x→1…

A: Limit exist at x = a If left hand limit = right hand limit lim x→a- g(x) = lim x→a+ g(x)

Q: 31. If f is continuous and f(3) = 9, which of the following statements must be true? (A) lim f(3x) =…

A: Here we define which statement is true or false.

Q: 3. Let f(x) = c.(x-4)+2 if 0 ≤x≤4 if x > 4 where c denotes a real constant. (a) Show that lim f(x) =…

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Q: x2-9 If f(x) = then f (x) discontinuous at x=3 because... ..... x-3

A: The function is said to be continues at x=a, if LHL(x=a)=RHL(x=a)=f(a) LHL - Left hand limit RHL -…

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: If 3x − 1 ≤ f(x) ≤ x2 − 3x + 8 for x ≥ 0, find lim x→3 f(x).

A: Here we use sandwich theorem Also known as squeeze theoremThis theorem states that , if gx≤fx≤hx in…

Q: if x1 then lim,-1 f(x) is 3 if x 1 (b) 3 3. Let f(x) = (a) 1 (c) not exist (d) other

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Q: Provide complete and clear solution for each question. Work Problem 2 ( +2 x²-x6 x²-100 x+10 B. Find…

A: 8

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: I(n) = ;n² - 글까-10 5-2t h(t) = t- 1 %3D S(h(0.5)) =

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