Vhich of the following functions is continuous on the interval (- 0, + ∞ )? @ f(x) =Vx²-1 B f(x)=(x²+1)(2r – 1) © f(x)=tan(x) x2+1 D s(x) =- 2х — 1

Q: ´28 – e14z x 0 Determine whether the function f(x) = 14x – 1

A: Solution: Consider the given function is  f(x) = x8-e14x    x<014x-1       x≥0 To check whether…

Q: тт Find the absolute minimum and maximum of f(x) = 2 sec x tan x on the interval [-- 4' 4

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Q: Is there a sequence of continuously differentiable functions: fn : R –→ R such that fn → x and f. →0…

A: Yes, the sequence is given in step 2.

Q: + [ƒ(2)₁ Suppose that fand gare continuous functions such that 1 [ g(x)dz -3, find f(x)dx= 2 and +…

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Q: (mx²- -3x+1 f(x) = x + 1 of function x=1 continuous at the х-1 X = 1 point of What should m and n be…

A: The given function is, f(x)=mx2-3x+1x-1,x≠1f(x)=n,x=1. That is,…

Q: if f(x) is a continuous function at x = -6 * = 0, then a 1- cos4x x2 If f(x)= { a x = 0 r>0 16+Vx-4

A: a= 8.   See the attachment for the complete solution.

Q: On which interval is the function f(x) = tan x² continuous Is the function f(x) = ! - continuous at…

A: 3.1)  tan x2 =sin x2cos x2We know that sin x2 and cos x2  are both continuous functions.Thus, tan…

Q: 1) Find the value of C that make the function continuous at x-1? x 1 -

A: We have given piecewise function  Function is continuous at x=1 if  f1+=f1=f1- f(x) = C-x        if…

Q: Give an example of a (discontinuous) function that does not satisfy the conclusion of the IVT on…

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

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Q: 9. If f is continuous and 1| f(x)dx = 8, show that f takes on the value 4 at least once on the…

A: We need to show f takes value 4.

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

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Q: VI. Suppose h' is continuous at x = 0 and h'(x) =tan(2x) - 1 if x > 0. Find h(0), if it exists.

A: Let's find.

Q: 1 x2 - х х x 2 Vx -2, Identify if the function g(x) is continuous/discontinuous at x=1. If…

A: Given: f(x)=1x2-x+1xx<0-10≤x<101≤x<21x=2x-2x>2 To determine: The given function is…

Q: (b)Consider the piecewise function S (1+ æ)ª – 1, if x>0 = (x) 6 I sin (4x), if æ < 0. Discover…

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Q: If f(x) =- 2-cos(x) sin(x) then the absolute minimum of f on the TI 3T is: interval O 2/2-1 O 2/2+1

A: Steps to find the absolute minimum value : Find the critical point of f Evaluate the function…

Q: 3. Find the constant k that will make f continuous on (-0o, 00). Sx – 4 , (kx2 – 24x + 46, x > 5 x<5…

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Q: (3) If the functions f(x) and g(x) are continuous 0sxS1, then f(x)/ g(x) is continuous on the…

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Q: x2 – 4x + 3 - f(æ) = 5. Let x - 3 How could we define f(3) x = 3? so that J is continuous at

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Q: f(x): at x = 3 X-3 f(x) = at x = 0 f(x)%3D%x6 at x - 0

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Q: Suppose that f(x) is a continuous function on the interval [0, π]. If f(x)=(sin x)² for 0<x<, then…

A: Given that the function fx=sinxx and the given function is a continuous function on the interval…

Q: 3. Find the value of k that will make f continuous on (-o, 00). NORS x + 19 if x 1

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Q: The Second Derivative Test cannot be used to conclude that x = 1 is the location of a relative…

A: Topic:- application of derivatives

Q: 1. Use the properties of continuous functions to explain why f(x) =x cos(x) +1 is a continuous…

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Q: 2 + 7x if x < 4 Let f(x) if x 2 4. For what value of the constant c is the function f continuous on…

A: Given function is: fx=cx2+7x       if x&lt;4x3-cx          if x≥4 We know that a function is…

Q: Find the value of K that make the functionf continuous at x=2 パ-4 マー3x+2 sin(rx) + kx + k if x > 2…

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Q: x2 – 1, if x 1 Let f(x) (a) Is y = f(x) continuous at x = 1? (b) Is y = f(x) continuous at x = 2?

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Q: 3. Find the absolute maximum and the absolute minimum of f(x) = x-2 tanx on the interval [0,4].

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Q: 5. Let f(x)= x . arccos x. Find f'(-/3/2) ||

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Q: [2x – 5] x if 0 3. - Determine if f is continuous or discontinuous at x = 0 and at x = 3. If di…

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Q: 20. The function f is continuous at x = 1. Vx + 3 -. - V3x + 1 for x 1 x - 1 If f(x) = k for x = 1…

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Q: 4x-8 i- -2 x +3a

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Q: 6- if f(x) is a continuous function at x = 0, then a = 1- cos 4x x0 V16+ Vx -4 3.

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Q: Find the value of K that make the function f continuous at x=2 -4 スー3x+2 sin(nx) + kx + k if x 2

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Q: Q3) If the function (2x + 1 +2 x > h) XSh f(x) having limit at x = h. Find the value of h. Q4) f(x,…

A: Our objective is to solve the above questions.

Q: 1. Does there exist a differentiable function f that is continuous on the closed interval [1, 4],…

A: Mean Value Theorem (MVT):   If f(x) is continuous on the closed interval [a, b] and differentiable…

Q: Find a nonzero value for the constant k that makes the function (tan(kx) x < 0 f(x) = Зх + 2k?, x 2…

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Q: Consider the function fcx) = (メフチ 5 E- xet X if x >5 if メ=5 5-X S> X f! Is fe) continuous at x=5?…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Suppose we know that f(x) is continuous and differentiable on the interval (-7,0], that f(-7)=-3 and…

A: fx is continuous and differentiable function on the interval -7, 0, f-7=-3 &amp; f'x≤2.

Q: Q.4 A/ Prove the function continuous at x = -2, (x2 + 5 13-3x where %3D if x<-2 if x 2-2 f(x) = %3D

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Q: 2. Find the (exact) values of a and b so that f is continuous at a = 2. 8r2 + 20x + 28 if x 2

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Q: x-1 for x 1 x -1 show that flx) is continuous at x = 1 !3! for x 1,

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Q: 4 '2 If f is continuous and f(x) dx = 10, find | F(2x) dx. %3D

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Q: Suppose f is a function such that f(z) = 4z' and f" (z) = 12z. Which of the following is TRUE? f has…

A: Suppose f is a function such that f'(x)=4x3  &amp;  f"(x)=12x2

Q: .3 Suppose that f is a continuous function and that f(x) dx = 6. Find f(3x)dx.

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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: Determine unknown constants a and b for which g(x) is continuous at x=1. [5x - 2 x 1

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