Find a value of c that makes Continuous extension the function 9x - 3 sin 3x 5x f(x) = c, continuous at r = 0. Explain why your value of c works.

Q: \S(cos x)dx = 0 %3D

A: Let us consider f is continuous even function. Let f=x2 So, fcosx=cosx2=cos2x…

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Q: (a) f(x) = sin(x) X at x = 0.

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A: ddxu(x)v(x)=v(x)ddx(u(x))+u(x)ddx(v(x)) ddx(sin(x))=cosx ddx(ln(ax))=aax=1x…

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A: The solution is given as

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A: Approach: Without wasting any time, take the derivative of the original function. Find critical…

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Q: What is special about the functions f(x) = sin x - 1 x + 1' x 2 0, and g(x) = 2 tan Vĩ? -1 Explain.

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A: We have to find the derivative of the given function.

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A: Given function is f(x)=x2sin1x0,     x=0,x≠0 By definition, f'(0)=limx→0f(x)-f(0)x-0

Q: Use the definition of a derivative to find f'(0) where: x² sin () lo x + 0 f(x) If the derivative…

A: follow next step

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Q: Consider the function f(x) whose second derivative is f''(x) = 9x +8 sin(x). If f(0) = 4 and f'(0) =…

A: Recall: ∫xn dx=xn+1n+1+c ∫sinax dx=-cosaxa+c ∫cosax dx=sinaxa+c ; where 'c' is an integration…

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Q: Some elementary functions, such as f(x) = sin(x2 ), do not have antiderivatives that are elementary…

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Q: Consider the function f(x) = sin2 (x) − sin(x), 0 ≤ x ≤ 2π. Find any x-intercepts of f(x) on [0,…

A: Consider the function f(x) = sin2(x) − sin(x), 0 ≤ x ≤ 2π.Find any x-intercepts of f(x) on [0, 2π]

Q: Q! O show th at [x sin'x + V1-x²] = sin'x sin x

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A: see 2nd step.

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Q: :Show that the function 1 x sin When x + 0 S(x) =- 0, is continuous but not differentiable at x = 0.…

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Q: Consider a function f(x) = (x ^ 6)/5 + sin 7x . Now using the idea of anti-derivative, find…

A: Integrating f(x)

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A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Find the root of the function f(x)=sin x +xe* between -3 and -4. using secant method ɛ = 0 %3D

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Q: Consider the function f(x) whose second derivative is f''(x) = 9x + 8 sin(x). If f(0) = 2 and f'(0)…

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Q: Use the Intermediate Value Theorem to show that f(x) = 2+ sin r 3 tan x has a | (0. ). solution in…

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Q: Differentiate the function. f(x) = sin(x) In(3x) f '(x)

A: Here, you can use the product rule for derivative. ddx(u·v)=u·v'+v·u'

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A: Given  f(x) = 5sin x We have to check the continuity of the function on the interval [0, 2π].

Q: Find f '(x) and f '(c). Function Value of c sin x f(x) %D C = 0 et

A: The given function is f(x)=sinxex            Differentiate with respect to x,

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Q: Hi, I need help with this step-by-step please.

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Q: Consider the function f(x) whose second derivative is f"(z) = 5x + 6 sin(x). If f(0) = 4 and f'(0) =…

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