If f and g are continuous on [a, b], then Lf(x)g(x)] dx f(x) dx (), 9. g(x) dx %3D a

Q: Suppose that the differentiable function y = f(x) has an inverse, that the graph of f passes through…

A: first we find equation of line which passes through (2,5) and slope (m)=1/4 y-5=m(x-2)…

Q: Let f (x) =e*· cos(x²). what is the correct result of the derivative of fwith respect to x? @…

A: Product rule of differentiation:     Chain rule of differentiation:

Q: Integrate (x)(e^-x)dx within the limits of (1, infinity)

A: Givne that  Integrate (x)(e^-x)dx   limits of (1, infinity)

Q: dy for all of: dx Find 3 x(x-2) 2- у %3 x2+1

A: We will use simple differentiation rules to solve this question.

Q: Find the implicit deriviate (dy/dx) of (2x+3y)1/3=x2

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Q: In(x) 1. Evaluate -dx if possible. If not possible, explain why.

A: As we know that the integration by parts:- ∫udv=uv-∫vdu

Q: Find f"(x) for a) f(x)= lnx - ln(1/x)

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Q: Find the dy/dx using logarithmic differentiation y=(x2(x4+5)1/2)/(ex-x^4) 2. Find the limit lim…

A: follow next step

Q: ential equati x²y dy = C

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Q: Given a function f with input that has the dimension [x] = L-M-T-1, such that [f(x)] = L-M, find the…

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Q: what is the derrivative of y^3 + y^2cos(x) = x^3 -3x and what points in the function for dy/dx does…

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Q: The derivative of the function f(x) =x ln x is: a. f'(x) = In x +1 b. f'(x) = ln x +. c. f"(x)= In x…

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Q: Find the solution and the interval of existence for: (1-x2)dy/dx + 2y = (1-x)2

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Q: The derivative of the function y = (3e* – x²)(cos x) is: a) y' = (3e* – 2x) cos x – (3e* – x²) sin x…

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Q: f(x, y) = 1/(xy), then the marginal pdf of X is (log x)/y. Is this statement True/False?

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Q: 6. f(x) dx = 2, find If f is continuous and xf(x2) dx.

A: given f is continuous and ∫09 f( n) dx = 2 we have to find ∫03 xf (x3) dx = ? we solve this by the…

Q: Evaluate f, f,(1-2) L(-dy dx dz

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Q: Find the finite derivative of a the functions below at x=1: a) f(x) = 4x³-3x²+2x-3 3 b) f(x)==-²/ 3…

A: Concept: The derivative can be represented as f'(x) or ddx(f(x)) Derivative of xn: ddx(xn)=nxn-1…

Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (2, 0).…

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Q: /4 - x2 the integral | dx, becomes

A: Given the integrationI=∫4−x2x2dx

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

A: let ∫x-necxdx for n a positive integer and c a non zero constant is non elementary since…

Q: Find the solution and the interval of existence for  (1-x2)dy/dx +2y = (1-x)2

A: The objective is to find the solution and existence for  1-x2dydx+2y=1-x2dydx+21-x2y=1-x1+x The…

Q: If f(x,y) = y2 ex + 3 ln (xy), find fxyy (1,1). fxyy (1,1) = ?

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Q: 2. Find the derivative (dy/dx) of the following functions: h) y = 3x7 – 7x³ + 21x² - i) y = (x² +…

A: As per guideline we have to solve first three subparts

Q: 6. Find [ f(x)dx if f(x) = et -1, if -3<x<0 V9-x², if 0<x<3

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Q: Let h be a function that has second derivative (x+ 1) (x – 2) (x + 4)e5 h"(x) Is x=2 the…

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Q: Find dy dx' i) f(x) = Cos2x Sin²x %3D ii) f(x) = log,(x' +4)* e-* /2x - 5 -3x iii) f(x): (6-5x)'

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Q: If f(x) = – x Find: S",(f(x))² dx That is find S"(: ,(1 - x)?

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Q: (a) Find the derivative. = In(x) – In(x - 8) dy dx (b) Find the derivative. y = In X - 8 dy dx %3D

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Q: - Use integration by parts to show that if f has an inverse with continuous first derivative, then…

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Q: Find all the relative and absolute extrema of the given function on the given domain f(x) = x^2 +…

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Q: a) In(x+1)³ dx x+1

A: Given, ∫23ln(x+1)3x+1 dx

Q: Use the chain rule to find the derivatives of f(x) and g(x) as well as f'(0) and g'(0): f(x) = (2x³…

A: According tp our guidelines we can solve only one question so we are solving 2nd question for you.…

Q: d 1+ tanhx - Show that dx V - tanh x

A: To show: ddx1+tanhx1-tanhx4=12ex2 Simplfiying 1+tanhx1-tanhx,…

Q: Evaluate the function: ( e* +1 dx et

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Q: Find the linearizationsof the following functions at x = 0. ln (1 + x)

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Q: Find the inflection points of the function f(x) = x 2 ln x

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Q: 4)Find the inflection points of the function . f(x)=ln(x^(2)+1)

A: In this question we will find the point of inflection   we have given function   f(x)=ln(x2+1)…

Q: dx = +C (x+1)² X+1

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Q: Evaluate the implicit function by finding dy/dx of x³+3y=3xy

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Q: What is the process for finding dy/dx when y is an implicit function of x? Illustrate with an…

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Q: The derivative of the function f(x) = 5+ ln r is: 1 a. f'(x) = 2.x/5+ In x b. f'(x) = 2/5+ In x In x…

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Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (2, 00).…

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Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

A: To determine the linearization for the function.

Q: Find oy for dx2

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Q: 1. If f(x, y) = sin(4x-2y)+ln(x²-2y) find fy fyx

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Q: Find the derivative of f (2) = xe 2 o f (2) = e * (e – 22) z- O f (x) = x°e-2# (;- 2) O (E) None of…

A: The product rule of differentiation states that d dxfg=fdgdx+gdfdx, where f,g are functions of x.…

Q: Use the second derivative f"(x) = x(x+ 1)(x - 2) to determine where the inflection points of f(x)…

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Q: Show that d/dx(ln kx) = d/dx(ln x), where x &gt; 0 and k is a positivereal number

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Q: Find the indicated derivative. dz if z = In (x° + e 5) dx dz dx

A: Given data is: z=lnx8+e5 To find the value of dzdx

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.