Find the values of the real constants a and b such that the function =-{ [ 1+ 2x + x²(5+ cos(1/x)) if x < 0, if x ≥ 0, f(x) is differentiable on R. a sin x + bcos x

Q: The maximum value of F in F(x) = - 4 cos x is 2 4 1

A: We know range of cosine function is [-1,1] Therefore maximum value of f(x)= -4cosx is, f(x)=-4cosx…

Q: Suppose we define a function f(x) by f(x) = a1 sin(x) + a2 sin(2x) +· + an sin(nx), .. for constants…

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Q: Letr> 2. Show that sin² r - sin² 2 r-2 < 2. Justify your answer. Hint: Apply the Mean Value Theorem…

A: Let r&gt;2.   To Show: sin2 r-sin2 2r-2&lt;2.

Q: xpress tiIE SS the f (x) = 3 sin? x + cos? x of oog m

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Q: ((sin? 3x +x² tan' x)dx x) dx 2

A: Value is zero

Q: (2) Let f(x) = -3 sin(x+2). (c) And then determine the domain and range of f(x).

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Q: Let a be a constant, Evaluate[ (a* + x² + a) sin(3z") + 15z*)dzr.

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Q: 2. If f(g(x)) = sin x + 3sinx - 1, determine possible expressions for f(x) and g(x), where g(x) # x.

A: (1st method/way): Let f(x)=x²+3x-1 and g(x)=sinx Then we can find f(g(x)) as follows…

Q: The interval(s) that contains the root(s) of the equation below is/are: cos +x² – 3x = 0 A. (-2,2) &…

A: Let's find.

Q: x sin wx dx x2 + 6x + 10 Show that (2 sin 3w – 3 cos 3w) w > 0 %3D - 2e2w

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Q: 3 - What is the domain of the function f(x) ? sin x + cos X

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Q: Show that the extreme values of f(x) = a sin x + bcos x tVa2 + b2. are

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Q: 5 g(t) = t(vE+ 1) 2

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Q: Verify that f′(x) = g′(x) and explain the relationship between f and g.

A: We have given fx=sin x-3xx, gx=sin x+2xx We have to verify f'x=g'x Quotient rule:…

Q: 2. (a) Show that if f analytic in a domain D, then it is independent of Z. (b) Solve the equation:…

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Q: f (x) = 3 sin x + 3 cos x, [0, 27]

A: Consider the function: fx=3sinx+3cosx Differentiate the given function with respect to “x” then,…

Q: Evaluate f x² cos 4x dx Evaluateſ sin* 3x cos3 3x dx Evaluate the integral J x²+x-1 dx x(x²-1)

A: Given:   i) ∫x2cos 4x dx      integrate by parts ∫fg'=fg-∫f'g     here f=x2,f'=2x , g'=cos…

Q: sec? r da = F(x)

A: Given- ∫0π4sec2xdx=Fxab To find- The value of Fx Identity Used- ∫sec2xdx=tanx

Q: The derivative with respect to x of 2 cos (x² + 2) is A. 2 sin (x²+2) cos (x² + 2) -2 sin (x² + 2)…

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Q: [1] S(4x³ + x)V4x² + 1dx > [2] S(2x7/2 – vx)* d. [3] S V1+ 2sin3xcos3xdx

A: As per bartleby guidelines we are support to answer only 3 subparts of a question. This post…

Q: Consider the function f(x) = sin2 (x) − sin(x), 0 ≤ x ≤ 2π.    Find the intervals of increase and…

A: Consider the function f(x) = sin2(x) − sin(x), 0 ≤ x ≤ 2π.  Find the intervals of increase and…

Q: Find approximate value of the derivative for f(wo)-6f(x1)+3f(x2)+2f(x3) fr(x2) = f(x) = 10 sin(20æ?)…

A: Introduction: Numerical differentiation is the technique of obtaining the numerical value of a…

Q: Show that if L{f(t)} = F(s) then L{etf(t)} = F(s - k) where k is a constant. Hence find: (a) Leat…

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Q: ifferentate: f(x) = COSX 1+sin x Apply the quotient ru

A: Topic:- application of derivatives

Q: Evaluate f dx V4 √4x²

A: This we directly computed by the rule of integration that is there is no any dificulty to find the…

Q: sing the relation r = Vn show that J_1(x) = COS X

A: We have to proof that given relation

Q: Find the anditerivative of the function f with the given condition f(x) = 0.528 - 4.5 sin(6.5x) and…

A: To find the anti-derivative of the function  with the given condition. and

Q: 4) More Complex Differentiation: Differentiate and simplify the following functions a) g(x)= rcosx…

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