Let f(x) sin x g(x) = x2 + 3 %3D %3D Evaluate the composite function (f og)(x)

Q: Given g(x) = ln[(x^1/3 + sinx - 3tanx)/3x^4 - x^1/2], calculate g'(x)

A: Given equation is , gx=lnx13+sinx-3tanx3x4-x12 Let's find g'(x) Formulae we are using here,…

Q: Find the absolute maximum and absolute minimum values of f on the given interval. a)…

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

A: a.the function is not defined at x=0. The function has right hand and left-hand limits same and…

Q: Differentiate the function. f(x) = sin(x) In(4x) f'(x) =

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

Q: Evaluate ∫(π ro −π) f(x)dx where f(x)={4x^2,   −π≤x<0 and 9sinx 0<x<pi

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Q: d Prove that (sin-l x) : dx V1 – x²

A: To show that:ddx(sin-1x)=11-x2

Q: f(x) = ln(cos3(2x+1)5)     f'(x) = ?

A: Given that f(x) = ln(cos3(2x+1)5)

Q: -T<x<0 Compute the coefficient Fourier ao of the f(x) = { 0<x<T

A: Since here we need to find only the value of the coefficient a0, so we use the formula: a0 =1L∫f(x)…

Q: 6. Differentiate. a) f(x) = In (sin²x) b) g(x) = In (xe-2*)

A: Write sin2x as (sinx)2 and simplify the terms and use the log property to simplify the term and…

Q: Find the absolute extrema of the function on the closed interval.                    f(x) = sin 2x,…

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

Q: dx Evaluate x²/4 x²

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Q: Find the family of antiderivatives of f(x) = sin 3x.

A: Given that f(x)=sin3x      ...(1)

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: Find f'a) for f(x)= =Sinx 1- Cos X %3D

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

Q: Differentiate the function. f(x) = cos(In(4x)) %3D

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Q: Find f'(x). f(x) = e- x arctan(x)

A: fx=ex-x3tan-1x

Q: Find (f-1)'(a). f(x) = 2x3 + 5 sin x + 3 cos x, a = 3 %3D (F-1)'(a) = %3D

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Q: f (x) = cos(x) f(x) = tan(sin(x)) g(x) = In(2x2 + 4x + 3)

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Q: y = In x' sin"x 3 X su X. ア=

A: The function given to us is  y=ln(x3sin2x)

Q: Determine whether a given function is homogenous or not homogenous: 1. f(x,y) = sin x 2. f(x,y) = x…

A: Since there is a mistake in third question i do first two question as per our company guidelines…

Q: Differentiate the function. f(x) = sin(7 In(x)) %3D f'(x) =

A: Given function :

Q: the specifie x = 1- y, x= 0; = 5.

A: In this question we will use basic of calculus i.e application of integration. We will simply use…

Q: 2. Differentiate the function. f(x) = e* tan x +7 cos x

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Q: 3. Evaluate f x sin2 (x²) dx.

A: Given I=∫x sin2x2 dx To Find I

Q: Given f(x) = ln(ln æ³) Diberi f(x) = ln(In x³) %3D 3 Show that Tunjukkan 1 f' (x) = xlnx %3D

A: Given that the function is fx=lnlnx3 and it is required to show that f'x=1xlnx.

Q: Let F(x) = / sin(8r²) dt. Find the MacLaurin polynomial of degree 7 for F(x). 0.6 Use this…

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Q: Let f(x) = x² and g(x) = sinx. The composite function (fog)(x) is equal to B. x² sin(x) C. (sin(x))²…

A: f(x)= x2 and g(x) = sinx  Find f(g(x))

Q: Find and locate the local and absolute extreme values of f(x) = x+(sin2x) in [0, π].

A: Find and locate the local and absolute extreme values of f(x) = x+(sin2x)in [0, π].

Q: • Let f (x) = cos(x). Use central-difference formula of order 0(h²) with step size h 0.1 , 0.01 ,…

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Q: Consider the function f(x) = x. 2 Compute (exactly) / f(x)dx and / f(x)dx using the graph off.…

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Q: [sin(In x) + cos(In x)]* dx 3. xp: 3x/10 In(3x) – (In(3x))²

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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)

Q: Find the linearization at x = a. f(x) = sin° (x), a = %3D (Use symbolic notation and fractions where…

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Q: Estimate cos(x²)dx by using a right-hand sum and 4 subintervals. |cos(x²)

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Q: Find the linearization at x = a. f(x) = sin³ (x), a = %3D (Use symbolic notation and fractions where…

A: Given fx=sin3x, a=π4 To find linearization at x=a

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'

Q: Consider the function f defined by f(x)=(e^x)(sinx) with domain [0,2pi]. Find the absolute maximum…

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Q: Estimate the value of df/dx for f(x) = root 8x at x = 3, using any method

A: To find the derivative of f(X), differentiate with respect to X on each side.

Q: f(x) = VT cos x2 COS 2x f(x) = x² + 4

A: Given functions is, f(x)=xcos(x2) So, differentiating it with respect to x, we get,…

Q: calculate the value : f'(x) 3. a) f(x)=4xe**+ln(sin/x)+2cos(x³ +2x+1)

A: f(x) = 4xex3 + lnsinx + 2cosx3+2x+1f'(x) = ?

Q: Find a value of c that makes Continuous extension the function 9x - 3 sin 3x 5x f(x) = c, continuous…

A: The given function is

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

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Q: Find the critical numbers of the function g(x)=8x+sin8x

A: Given data: The expression for the given function is g(x)=8x+sin8x. The differentiation of the given…

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

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Q: If f(x) = 4 cos x – 6x, find the relative percentage error in f(x) for x=0, if the error in x is…

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Q: 3 Find the maximum and minimum values for f(x) = - 4-(/2 cos x - V2 sin x)

A: Topic = Functions Maximum value of f(x)=1.5 Minimum value of f(x)=0.5

Q: Find the linearization at x = a. f(x) = sin°(x), a = 4 (Use symbolic notation and fractions where…

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Q: k. f(x)=cosh(x³)+ sinh(10x) 1. f(x)=In(x* +1)

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Q: alue of A can be calculated based on f(x)dx = 1.

A: The given probability distribution function is,