Examine if f(x) = ln(x2+2) is uniform continuous on the interval (-∞,∞)

Q: Prove that f(x)= 2x-tan^1x-ln(x+√x^2+1) increasing on [0, infinity]

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Q: Find the critical point and the interval on which the given function is increasing or decreasing,…

A: Explained below

Q: find the absolute maximum and absolute minimum values of ƒ over the interval. ƒ(x) = (4/x) + ln x2,…

A: Given,

Q: f f(x) = ln(x2+10x+16) ov

A: The absolute minimum of f(x) is 6ln(2) and the absolute maximum of f(x) is 4ln(2)

Q: 2. Let g(x) = x – 3x 3 . (a) points of g(x). Determine the critical Use the Second Derivative (b)…

A: To find- critical points, local extrema and inflection points of g(x).

Q: Determine if the function f(x)= is continuous -- sin(x) x on the interval I= (0,1).

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Q: 67. Is the function given by g(x) 1 continuous over %3D x + 5 the interval (-4, 4)? Why or why not?

A: g(x)=1x+5

Q: Proof the n + 1 derivative of xk is zero, where k <n

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Q: Determine the intervals where the function f (x) = x ln x (x 7 0) is increasing and where it is…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = ln(x2 + 5x…

A: The given function f(x) = ln(x2 + 5x + 13),    [−3, 1] Differentiate with respect to x…

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x ln…

A: Now differentiating with respect to x, we get

Q: 12. Show that x sin(1/x), if x#0 f(x)= 10, if x = 0 is continuous but not differentiable at x = 0.

A: The given function is fx=xsin1x, if x≠o0, if x=0. Show that the given function is continuous but not…

Q: ( 2x -. Is g(x) continuous at 2?

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Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x2 ln…

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Q: -2 Find the interval(s) where f(x) =- 64-x2 is continuous.

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Q: a. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and…

A: fx=xlnx Differentiating with respect to x, we get f/x=dxdxlnx+dlnxdxx    Because,…

Q: Using the (e- 6) definition, show that f(x) = 3x – 1 is continuous at point x = 1.

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Q: x 0 entiable at x = 0.

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Q: 5. Prove f(x) = e* + x has a root on the interval (-1,0) using the Intermediate Value Theorem.

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Q: Let f (x) =e* - sin(x²). v What is the correct result of the derivative of f with respect to x? A…

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Q: Apply the Mean Value Theorem for the function f(x) = 2 ln(4x + 7) over the interval [1,3]. Show your…

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Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (2, 0).…

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Q: 5. Find the exact absolute maximum and absolute minimum values for f(x) cos(x) + sin (x) on the…

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Q: 3. f(x) = Vx - 5 is continuous on the interval [5, 0) %3D

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Q: 4. Verify the Mean Value Theorem for the function y=ln (2x + 3) in

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Q: FIND a) F(5) b)interval over which F(x) is decreasing  c) what x=? Where F(x) has a maximum value

A: Given, F(x)=∫0xf(t)dt Graph,

Q: Use the e - S definition to show that the function x- 1 f(x) = x +2 %3D is continuous at x = 3.

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Q: 5. Use the limit definition of the derivative to find the derivative of f(x) = 3x-2. f(x+h) - f(x)…

A: f'(x)=limh→0 f(x+h)-f(x)h

Q: A continuous function f satisfies the equation 1 f (x) = x – t+ 2 f(t) dt 0, For all x e [-1, 3].…

A: We have to use leibiniz rule of  differentiating definite integral  d∫f(x)g(x)h(t)…

Q: Left- and right-continuity a. Is hlx2 = Vx - 9 left-continuous at x = 3? Explain. b. Is h1x2 = Vx -…

A: To Determine: find left hand and right hand continuity at x=3 and explain this Given: we have a…

Q: Verify Mean value theorem for the function f(x)=4x3+x+2 over t interval [0,1].

A: Prove hypothesis of mean value theorem Differentiate continuous and value of c

Q: A function f has derivative f′(x)=x^3(x−1)^2(x+1)(x−2). At what numbers x, if any, does f have a…

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Q: Find all the relative and absolute extrema of the given function on the given domain f(x) = x^2 +…

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Q: How must f(0) be determined so that the function f(x) = x2-x ニー x0, is continuous x-1 at X= 0?

A: Let f be a real function . Let a be any point in its domain . If limx→afx exist and equal to fa Then…

Q: Find the intervals on which f is increasing and the intervals on which it is decreasing. f(x) = - 2…

A: Given, f(x) = 2cox - x              x ∈ [ 0 , 2π] f'(x) = 2 (-sinx) - 1 = -2sinx -1…

Q: (NAS) Find the local linear approximation L (x of the function f (x) = x² + 3 at : 1 [SADT] Using…

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Q: find the absolute maximum and absolute minimum values of ƒ over the interval ƒ(x) = x - 2 ln x,…

A: The given function and the interval is,

Q: f(x)= X-I x=1 √x-1 X = 1 1123 -s continuous at x = 1?

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Q: x20 is continuous at x-0, then a = a+sinx If the function f(x): 2+2acosx x<0 a. 1 b. -1 O c. 2 d. -2

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Q: f(x+h)-f(x) For f(x) = x- + 2x, use the definition of the derivative f'(x) = lim h→0 to find f'(x).…

A: Using the definition of derivative formula,

Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (2, 0).…

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Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x2 -…

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Q: Consider the function f(x) = x - 3 ln(x) on the interval The absolute maximum value is and this…

A: Consider the given function, fx=x-3lnx differentiate the function with respect to x,…

Q: Let g be a function that has derivative x(x – 3) (x – 5)e2" g'(x) = Does x=3 belong to a local…

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Q: Find the value of a which makes the function below continuous on (-∞, ∞). f(t) = [a(x²/2) x < 1…

A: We will use the definition of continuity to solve this question.

Q: Prove that f(x) = x-¹/2 is: (i) not sectionally continuous in every finite interval in the range x ≥…

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Q: f(x)=12+4x-X ', [o,s]

A: We will use derivative test to find the maxima and minima.

Q: The limit represents the derivative of some function f at some number a. State such an f and a. V81…

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Q: Q. 1: Determine the func- tion is continuous or dis- continuous at x = -1 and x = 1.

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Q: Find the x-value for all relative extrema of f(x) using the first derivative test. 1+x + x² f(x) =…

A: Given: The function is  fx=1+x+x2x2+x-2   To determine: The x value for all relative extrema of f(x)…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.