If f(x) is continuous on R, then |f(x)| is continuous on R.

Q: *You must fully justify your answer* A continuous function f satisfies the equation f (x) = x – f(t)…

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Q: (x2 -7 , 0b Is fdifferentiable at b?

A: Given that: f(x)=x2-7,       0<x≤b6/x   ,        x>b

Q: Determine if the function f(x) is continuous and/or differentiable at x = 1? x +5 for - 1sxS1 f(x) =…

A: The given function is f(x)=x+5    for -1≤x≤16x       for  1>x≤4 The function is said to be…

Q: Lel f(x) = 2x (x² - 3x x 5 (a) Is f continuous at x = 5 ? (b) Is f differentiable at x = 5 ? (c) If…

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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: 4x -5x-6 for x +2 Given f(x) 2-V2x 4 for x = 2 Is the function f continuous at x = 2 ? Give…

A: A function f(x) is continuous at x = a if limx→a+f(x)=limx→a-f(x)=limx→af(x).

Q: a. On what interval(s) is f(x) increasing? Justify. b. What is the concavity of f(x) at x=2?…

A: Part(a). From the given graph f(x) is increasing on the interval (-4,1) , Because f'(x)>0   (…

Q: True or false? Explain. The function f(x)=x² is invertible 1S

A: A function is invertible if we can establish one to one function such that two input can't have same…

Q: x+2, The function f(x) = 2x², Select one: Ⓒ True False x≤1 1<x<3 is continuous from the right at x =…

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Q: 3. Consider the function for x +0 f(x) = for x = 0. (a) Would you expect S f(x) dx to be defined?…

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Q: Sx' - 3, xS2 lx² +1, x>2 a. Is h continuous at x = 2? b. Is h differentiable at x = 2? 2. Given that…

A: A function is continuous at a point if the limit of a function at that point is equal to the value…

Q: x- 1 f(x) = x + 2 %3D is continuous at x = 3.

A: Check function is continuous or not at x=3

Q: x² – 16 tate why f(x) is continuous on [1, 2]. x² – 9

A: f(x) is continuous on [a,b] if and only if  1. ∀x0∈(a,b)⊆R, limx→x0f(x)=f(x0) 2. limx→a+f(x)=f(a)…

Q: g'(x) a. On what interval(s) is g increasing? How do you know?

A: Definitions with respect to the function help to determine the required for the function graph. A…

Q: 1 is uniformly continuous. 1+x 5. Clarify that f :R→R defined by f (x)=

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Q: Find a value of c that makes the following function continuous at x = 0. Explain why the value of c…

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Q: a. Graph the function 0 Sxs1 12 - x, 1<x< 2. X, f(x) b. Is f continuous at x = 1? c. Is f…

A: We have to find out the given function is continuous and differentiable at x=1 or not.

Q: x² + 1, x 1 Let f(x) = Is function f continuous at x = 1? Is functionf differentiable at x = 1?

A: Given :-  f(x) = x2+1 when x&lt;1  f(x) = 4-2x when x≥ 1  To find:- Check function continuous or…

Q: Find a value of c that makes the following function continuous at x = 0. Explain why the value of c…

A: Given that, f(x)=15x-5sin3x2x3, x≠0c,                          x =0 The function is continuous when…

Q: In the space below indicate the absolute extrema on the interval [-3,2] for f(x) = (x− 1) ^2/3

A: givenf(x)=(x-1)23 then f'(x)=2(x-1)-133=23(x-1)13f'(x)=0then23(x-1)13=0so there is no critical point…

Q: Vx+5 14. f (x) = ;(-5, —4)аnd (-2,4) | х2+6х+8

A: On the given interval the function is continuous.

Q: Using the definition f'ex) = li fCxth) -fcx) find f'(x) when fex)

A: Here we have to find f'(x) using definition.

Q: What can you say about the function f(x) = |¤|? %3D Select one: O a. f is differentiable but not…

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Q: |x? +3x +1 ax + In x+b ,x21. „r<1; Let f(x) = If function f(x) is differentiable at point x=1, then…

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Q: I'm having trouble understanding the continuity questions, please see the attached screen shot.

A: We find left and right hand limit at x=0.Left hand limit = 1

Q: function f(x) such that f'(x) = (2x – 1)e²“. O Find the interval/s on which ƒ is increasing /…

A: Explanation: Given that,                          find the critical points to put the f'(x) = 0…

Q: 15 f(4) = 15, f' is continuous, and f'(x) dx = 19, what is the value of f(5)? %3D inuoc 23

A: We have to find function value

Q: {x + 1, x < 4 lx - 4, x 2 4 Let f(x)= a) Explain why f is (or is not) continuous at x = 4. b)…

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Q: (c) Simplify the function f(x) = |x - 1|+ |x + 1|. Test the continuity of this function at x 1. At…

A: f(x)=|x-1|+|x+1|, for all x∈ R, It can be written as f(x)=-(x+1)-(x-1),       x&lt;-1(x+1)-(x-1),…

Q: 2x, x > 1 Let f (x) = ,where a is real. What value of a will make f -x + a, x < 1 1? continuous at X…

A: Let's Solve, Answer : Option B

Q: 10 If f is a continuous function and F'(x)=f(x) for all x € R, then dx=? @2[F(5) – F(1)] ®2[F(10) –…

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Q: Sx²-x²+1 1-sin x if x20 ) Let f(x) be defined as f(x)={* 0>x Is f(x) differentiable at x = 0? a) Is…

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Q: Find and interpret f'(2) and f''(2). f(x) = - 2x? f'(2) = f''(2) So at x = 2, f(x) is | decreasing v…

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Q: 7. If f(4) f '(x) dx = 15, what is the value of f(7)? 14 11, f'is continuous, and %3D f(7) =

A: Given

Q: х-4 ,x5 Given: f(x)= , find the value of k that will make f continuous on (-0,) kx2 – 24x + 46 , x>5…

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Q: 4 If f(1) = 14, f'is continuous, and f '(x) dx = 19, what is the value of f(4)? %3D f(4) = %3D Need…

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Q: TRUE OR FALSE. a) f is increasing on (-∞, -3). (b) f is differentiable on x = -3. (c) f" is…

A: A differentiable one-real-variable function is one that has a derivative at each point in its…

Q: &r4- V iderivative of F (x) =- determine the value of C (use 3 decimal places, answ

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Q: ( cx2 + 3x if x < 2 Let f(x) - CX if x 2 2. For what value of the constant c is the function f…

A: cx2+3x       x&lt;2x3-cx      x≥2For a function to continious limx→2-f(x) = limx→2+f(x)when…

Q: 4. For each part, find a real value c that makes f continuous at x=0, if possible. If not possible,…

A: A function is continious , when at that point limit of the function exists , and thatlimit is equal…

Q: - Is the function given by f(x): X the interval (-7, 7)? Why or why not? +3 continuous over

A: Topic:- function

Q: -3 Let f be a continuous function such that f(x) dx = -6 and 10 10 1 f(x) dx 3. What is the value of…

A: Given integrals are ∫-2-3fxdx=-6∫-210fxdx=3

Q: Find the absolute extrema of the function f(x) = x?e-z on the interval %3D

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Q: find the absolute extrema for f(x) = x^2/3 (2-x) on [-1,2]    please show all work

A: To calculate the critical  extreme values for the given function over the given interval

Q: Show that f is continuous on (-0, 0). S1 + x² f(x) : if x 1

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Q: Determine where the function f(x) is continuous. f(x) = Vx- 8 The function is continuous on the…

A: fx=x-8 The domain of given function is the set of all values of x for which x-8≥0⇒x≥8⇒x∈[8, ∞) Let c…

Q: You want to determine if f (x) dx converges or diverges. You find a function g(x) such that 0 < f…

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Q: j) Differentiate your formula for f-(y) to get a formula for (f-1)'y)

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