Consider the function f(x) = 8+ (In(z² – 4))* What is its domain and range? (Use interval notation: U for union and INF for oo).

Q: Integrate f(x) from x = 2 to 8 using Three-Point Gauss-Legendre Quadrature. f(x) = 5000+24563x -…

A: Gauss legendre quadrature gives the result of integration over a symmetrical limit of variavle x…

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

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Q: use the second derivative test to find the local exterma of the function  f(x) =x3-9x2-48x+72 on R

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Q: : Apply Rolle's theorem for the function f(z) = 7x² – 28z+ 21 over the interval [1,3]. er.

A: The given function is, f(x)=7x2-28x+21 over the interval [1,3]. Observe that, the given function…

Q: Verify Rolle's theorem for f(x) = x* – 4x+8 over the interval [0, 2].

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Q: Find the constant a such that the function sin x -13 - S(x) = %3D a+ 11x, x 20 is continuous on the…

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Q: Find the constant a such that the function is continuous on the entire real line. [ 5x², x 2 1 x < 1…

A: The given function is: f(x)=5x2   ,   x≥1ax-3,  x&lt;1 To find constant 'a' such that the function…

Q: Does the MVT apply to f(x) =- x²_3x+5 on the interval [-1, 2]? (x-1)

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Q: The function f(x,y) =26-2x²-y² is continuous at point (2, -3). .A True .B False

A: The objective is to determine whether the statement, " The function fx,y=26-2x2-y2 is continuous at…

Q: use the second derivative test to find the local exterma of the function f(x) =x3 -9x2-48x+72 on R

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Q: Define the function f(x, v) = 4x³-x³y-4y5 3x5-3y5 at the origin so that it becomes continuous there.

A: A function is said to be continuous at (a,b) if the the value of function at (a,b) is equal to…

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

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Q: Q1: If the function f(x) define as f: R→ R such that f(x) = (x+1, x>2 x²-1, x≤2 Show that the…

A: This is the question to check the differentiability of the function.

Q: let f(x) =x2 , on interval 0<x<2n, sketch

A: We have to sketch the graph of the function f(x)=x2 on the interval 0≤x≤2π.

Q: Find the absolute extrema of f(x) = 6x + 4 + on the closed interval [1, 6). Show all work.

A: Absolute extrema at x=2 and 6..

Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

Q: differentiate the follouwing 243 a) f(x)=2x°-in/x|+3 arccos (X)

A: Since you have asked multiple questions in the same request, as per the policy, only the first…

Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = e - x 2

A: Consider the given function. fx=e-x2 The function is define for every real value of x. Hence,…

Q: Integrate f(x) from x = 0 to 10 using Three-Point Gauss-Legendre Quadrature. f(x) = 5000+24563x -…

A: Given f(x)=5000+24563x-7418x2+768x3-31x4+0.14x5 Let I=∫010f(x)dx Here a=0 and b=10

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: f(x) = Vx-3

A: Given function is fx=x-3.

Q: 6. Use the definition, determine whether the function g(x) = x = 2. Justify the conclusion. x² -…

A: The solution is given in the next step.

Q: Find the local maximum value of f using both the First and Second Derivative Tests. f(x) = x + V1 -…

A: First calculate critical point at which either local maxima or local minima will occur by putting…

Q: Find the domain of the function. Express the exact answer using interval notation. f(x) = To enter…

A: Consider the function  f(x)=25x+8

Q: Determine where the function F(x)=8x/x2+4 is continuous. The function is continuous on ?

A: Suppose   are continuous function at then rational function is continuous at   if .

Q: . Find the maximum value of f(x) = In(x – In x) on the interval -sxs. Show all steps .

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Q: Find a function flx) such that f(x) -llex and %3D 3. f(0)-- 주

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Q: Consider the function f(x) = 1 - 7x² OI function on this interval, i.e. f(3)-f(-4) 2 4)

A: answer is in next step . please give a like !!

Q: Find a function f(x), such that f"(x) = 3sin(4x). %3D

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Q: Find the constant a such that the function is continuous on the entire real line. (8x?, lax – 6, x2…

A: Given function f(x) = 8x2-x≥1ax-6, x&lt;4we find constant 'a' such that the function is continuous…

Q: Use the intermediate value theorem to show that f(x) = e-x2− x has at least one root in the interval…

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Q: 3-The function f defined by 2. Is f is Continuous at x=| ?

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Q: Find all points c satisfying the conditions of the MVT for the function f(x)=x3−x in the interval…

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Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

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Q: Find the value k that makes the function continuous. Ska², f (æ) = x > 2 kx + 12, x < 2

A: Topic - continuity Function is continuous If its left hand linit is equal to right hand limit and…

Q: Show that the function f(x) = 1 – I - x² is continuous on the interval [-1, 1].

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Q: Find the domain of the function using interval notation. f(x) = -2x (1- 1) (r – 7) To enter oo, type…

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Q: Find all the x-intercepts of f(x)=cos(x) on the interval [0,2π)

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Q: Find the constant a such that the function is continuous on the entire real line. (9x², Flx) = {9x?,…

A: Given function is : fx=9x2    ,      x≥1ax-6   ,    x&lt;1 Here given that function is continuous…

Q: Describe the domain and range of the function. f(x, y) = In(xy-1) Dor

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Q: Is the function f(z) = (x2 - y2) + 2xyi entire? Why or why not?

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Q: The function f (x) ,x € [-27, 2n] is continuous on: 1-cos x

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Q: (c) Determine whether f (x) is continuous at x-2, where [4x+3, xs2 f(x)= 8-x, x2

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Q: Use the chain rule to show that for any differentiable function f(x) > 0, f'(x) [In(f(x))]' = f (x)"…

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Q: Is the function F(x) as given is constant, increasing, or decreasing on the interval (0, ∞)?…

A: Fx=∫x2x1t dt⇒Fx=lntx2x⇒Fx=ln2x-lnx⇒Fx=ln2xx          ∵lnx-lny=lnxy⇒Fx=ln2

Q: Verify Rolle's theorem for f(x) = x² - 9x +6 over the interval [0, 3].

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Q: defines 2 as y. y- cos (3x2) = 5 a function of x and • differentiate implicity to find az ду

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Q: Determine the interval(s) where f(x)-In (5x+10) is continuous. It is continuous in the interval

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