r. xis rational x is irrational. (0. x Show that f is differentiable at x- 0. . Let f(x)

Q: Sx², lo, (0, x is irrational. x is rational Let f(x) Show that f is differentiable at x = 0.

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Q: Find the absolute extrema of the function f (x) = 30x – x² over the interval (-o, 00)

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Q: Let g : R → R be defined by Jx2 + x, if x is rational g(x) 10, otherwise. The function g is…

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Q: a. Find the value of (k) that make fhe fimction contimuous at x = 0 3k -3 =0

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Q: Suppose that f(x) is a differentiable function such that f'(8)=7 and f(8)=1. If g(x)=cos(f(x)), then…

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Q: Evaluate the definite integrals using the graph of f (x) below. 6. 4- y 2- 10 12 -2- -4- (a) f (a)…

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Q: P(z) how might the function 9(x) Question 3: When working with rational functions of the form f (x)…

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Q: c) lim,→1+ f(x) where f(x) = { V1- x, x 1 | x +1,

A: Given query is to find indicated limits.

Q: Suppose that f(x) is a differentiable function such that f(8)=5 and f(8)-D0. If g(x)=sin(f(x)), then…

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Q: 1) Find the absolute extremum values of f(x) = x? [1, 2]. 2x +24 over the interval %3D -

A: Topic - maxima minima

Q: 1. For f (x) defined below, at what values is f discontinuous? if x < 0 (sin x, 1, if x = 0 f (x) =…

A: Solution

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: и(х) -f(x) 1(x) 1.5 + 2 3 4 In the figure, is f(x) squeezed by u(x) and (x) O 1. at x = = 3? ? 2. at…

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Q: 8. For what value of the constants A and B is the function f continuous on (-∞, ∞)? Ar + B for r 2

A: Please see the the answer below.

Q: 1. Suppose that f f(x) dx = In x + Vx+1+C. Can f be a rational function? Explain.

A: To explain f is a rational function or not.

Q: dx For - = In[F(x)]+C• What is f(/3) if C = 0? (x+x³) (x Tan-'x + 1) -1 - 6. + -1 - -15 -is -is

A: Integrate ∫dx(x+x3)(xtan-1x+1)

Q: Find (a) the intervals of increase or decrease, (b) theintervals of concavity, and (c) the points of…

A: fx=1-xe-x Differentiating with respect to x, we get…

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: Define f:R → R by f (x) = 5x if x is rational and f (x) = x² + 6 if x is irrational. Prove that f is…

A: Given, f:R→R by f(x)=5x if f(x) is rational and f(x)=x2+6 if x is irrational.To prove that f is…

Q: 7. For the function f(x) = In(a? + 1) (a) find all intervals where f concaves downwards

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Q: 1. Determine the absolute extremum values of f(x) = x? / 2x + 4 on [-3, 1].

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Q: -x² +1 1- sin? x if x20 if x <0 Let f(x) be defined as f(x)= • Is f(x) differentiable at x = 0? • Is…

A: Answer and explanation is given below..

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: Given the function of f(x)=sinx- cosx at x = 2 and h = 0.5 What is the value of f(x;)? 0.33254…

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

A: Given: fx=-2cosx-2x; x∈0,π we know that any given functionfx is increasing in a interval if f'x is…

Q: Show that the function is continuous only at x = 0. (Assume that k is any nonzero real number.)

A: The given function is fx=0    if x is rationalkx   if x is irrational where k is nonzero. Note that…

Q: (b) Given -3x + P for x7 Determine the value of p if f(x) is continuous at x=7. TEST DMI123

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Q: - Find f (x) given f' (x) 6x2 - 4x + 3 and (2, 15) is on the curve of f (x) .

A: To find the function from derivative we need to integrate.Here we will integrate to find f

Q: Consider f(x) = #3/5. Is f(x) differentiable at x=0? Is f(x) continuous at x=0?

A: The given function is,

Q: 2. For which values of a is f(x) differentiable on R?

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Q: III. Let f(x) = e2 sinz 2. Find the absolute extremum values of f on the interval [

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Q: Consider the function: { 0 ;if x is rational ; if x is irrational f(x) = Use a d, e argument to…

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Q: (x+1, l-x +1, x >0 Is f(x) continuous at x = 0? x30 Suppose f(x) =

A: We find the left-hand limit, right-hand limit and the value of f(x) at x=0

Q: a. Find the value of (k) that make the fumction flk) = ,continuous atx = 0 +3k-3 x=0

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Q: Since the simplified numerator, >0 for all X, we have "(x) > 0 x²-1>0 e ]x > and f"(x) < 0 X| < Thus…

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Q: The interval on which f(x) = VI-x is decreasing where x€ [-1.1] is

A: Given function f(x)=1−x2   on  [−1,1]

Q: - 35) Prove that if y=flx)is continuoUS and flx1= 0 when x is a rational number, then f Lx)=0 for…

A: The objective is to show f(x) =0 for all x belongs to R.

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: Let f be the function defined on [0, 1] by when x is irrational, f (x) = 1 when x is rational.…

A: Please see the below picture for detailed solution.

Q: Find the absolute extrema of f (x) = x-12x on the closed interval [0, 4].

A: The given function is, fx=x3-12x The interval is 0, 4

Q: Jx?, x is rational 1o, x is irrational. Let f(x) Show that f is differentiable at x = 0.

A: Given, We know that, fx=px     , x is rationalqx     , x is irrational  is differentiable only at…

Q: Let f(x) = e2sinx 1. Find the absolute extremum values off on the interval [7]

A: To find the extreme values of given function at given  interval.

Q: * Suppose -x if x π - (a) Find f'(x) (b) Find f"(T) or show that f is not twice differentiable at 7

A: Given Function  f(x) = -x    if x&lt;0sinx  if 0≤x≤ππ-x  if x≥π   a) i) we have to find f'(x) at x=0…

Q: ber vals Of Vity, allU inflection points for the following function. f(x) = In(2+ sin(x)), on [0,…

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Q: dx - = In[F(x)]+C• What is F(/3) if C = 0? For (x+x³)(x Tan-'x+1) -1 + - 3 -1 + - 3 -15

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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: If f (x)  =In  (2x + x Sin x), use the graphs of  f ,f' , and f"to estimate the intervals of…

A: Given: f(x) = ln(2x+xsin…

Q: 3. What value of k would make f (x) continuous at x = 3 ? 3.

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Q: Q20: . Suppose that f(x) is continuous and differentiable on the interval [0,6], that f(6) = -7 and…

A: Given that the function “f (x)” is continuous and differentiable on the interval [0, 6] that, f (6)…

Q: H.W Ex 2: Determine if the f(x) is continuous at x = 3 ? [x² – 1 f(x)=- |x² + 2 at x=3 at x+3

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