1. Let f: (0,00)→ R be a differentiable function such that lim f'(x) = 0. x+00 Prove or disprove that lim [f(x + 1)-f(x)] = 0.

Q: Give an example of two differentiable functions f(x) and g(x) such that: lim, 00 f(x) = lim, 0 9(x)…

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Q: Carefully sketch the graph of a continuous function f which satisfies the following properties:

A: Given, Sign of f'x-f'x<0 on an interval -∞,-2. f'x>0 on an interval -2,0. f'x<0 on an…

Q: Use the Squeeze Theorem to find lim f(x), given that 4 − x − 2| ≤ f (x) ≤ 4+|x − 2]. x→2 lim f(x) =…

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Q: Let f be a function such that −x^2 < f(x) < x^2 for the interval [−10, 10]. Does the squeeze theorem…

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Q: Which of these is the limit definition of the derivative of f(x)? O f'(x) f (x + h) – f (x) lim h 00…

A: use the basic definition of derivative to choose the correct option

Q: Let f (x) and g(x) be differentiable functions in (a, continuous at a and b, and g(x) #0 in [a, b].…

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Q: If it is continuous, there are 3 conditions needed to be satisfied: i. f(a) is defined ii. lim x→a…

A: The three criterias that you have mentioned are for a point. When we check the continuity at a…

Q: 2. Let f(x) be a continuous function on R. The following is known about f(x): • The domain of f(x)…

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Q: x² 1) Let f(x): = (Figure 24). Verify the following: x - 1 (a) f(0) is a local max and f(2) a local…

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Q: 3) If the lim f(x) = 2 and lim f(x) = -1 %3D x-3- x-3+ Then what is the lim f (x) = x→3 %3D a) Why?

A: To find the limit of the f(x) at x=3

Q: 61. Let f(x) = x/x for x > 0. (a) Calculate lim f(x) and lim f(x). (b) Find the maximum value of f…

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Q: Differentiate the function f. Use the form f'(x) = f(x) = 9x² + x + 8 f'(x) = = lim h→0 f(x +h)-f(x)…

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Q: L True False y -2 then x 1 lim f(x) = 0 y = f(x) 3 X

A: We have to find Lim x approaches to 1 f(x)

Q: 11) If f is a continuous function such that f(2)= 6, which of the following must be true? f(x)-f(2)_…

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Q: ƒ(0) = 0, and ƒ'(−2) = f'(1) = ƒ'(9) = 0 ● lim f(x) = 0 and lim f(x) x →∞ x→6 • f'(x) 0 on (-2, 1)…

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Q: State the function and the number: f(x) = a =

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Q: Sketch the graph of a function that satisfies all of the following conditions. Explair • f(0) = 0,…

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Q: Let f: RR be a function that is differentiable on (a, o), where a is any real constant. Let g: RR be…

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Q: 83. Let f(x) = In (1 – x²). (a) State the domain of f. (b) Find f'(x). (c) State the domain of f'.…

A: Since you have asked multiple question and have not specified any question in particular, I will…

Q: lim f(x)=-5 f. f'(-3)=0 а. g. f'(-2) is undefined h. f(-1)=2 i. f'(-1)=0 j. f'(3)=0 b. f'(-5) is…

A: When there's no tangent line and thus no derivative at a sharp corner on a function

Q: Consider the function (a) Compute the derivative of f(x) directly from the limit definition.…

A: We will use the given information to solve the given questions

Q: Find the limit of the function f(x) = x²esin(1/x) as x approaches to zero.

A: To find limit of function f(x)=x2esin(1/x) as x approaches to 0. (Using Squeeze theorem)

Q: Let F (x) = { tan (x − 3) x < 3 x-5 3 ≤ x Then lim F(x): x 3- = CH M₂ 146

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Q: 7. Explain why for any function g, limg(c +h) = lim g(x). Use this to show that f'(c) = lim f(x) –…

A: Consider the given function limh→0gc+h=limx→cgx

Q: A tank contains 70 kg of salt and 1000 L of water. A solution of a concentration 0.035 kg of salt…

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Q: Sketch the graph of a functionf that satisfies all of the given conditions: 1) f(0) = 1, f(2) = 3,…

A: Graph is given below:- You can verify all the conditions.

Q: 3. Define f(x) so that S(2) = {ap(). f(x) = 0, |피 1 (a) Explain why the function f(x) must be…

A: As per our guidelines we can answer only 3 subparts. please ask others seperately.

Q: Suppose f(-2)=0 g(-2) = 0 f'(-2) 5 g'(-2)=1 = and all functions are continuous. f(x) lim Z-2 g(x)

A: The given values are .To find the limit .

Q: Suppose that in the interval 13 ≤ ≤ 19 you know that negative. Select the correct comparison. lim…

A: The given data is: y=f(x), 13≤x≤19