f(x) = x³ – x +1 e = 0.0001 %3D %3D initial value = 0 %3D increment = -1 %3D

Q: these equations have complex characteristic roots. Find the general solution in each case.  a.y'' +...

A: NOTE: Refresh your page if you can't see any equations. . for the homogeneous system, the auxiliary...

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Q: Find the area of the triangle with the given vertices.     (−1,−1), (5,−1), (2,5)   The area of the ...

A: Area of triangle = 12x1y11x2y21x3y31 x1,y1=(-1,-1)x2,y2=(5,-1)x3,y3=(2,5)  

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Q: I Find the second derivative(y") of the following functions and simplify the final result 1. y = x –...

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Q: 3. Consider the following surface and the point Pon the surface. Let C'be the path of steepest desce...

A: f(x, y)=y3 - x2∇f =fx, fy =-2x, 3y2Descent = -∇f =2x, -3y2This can be put as;that the slope of the d...

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Q: Using spherical coordinates to evaluate the triple integral zdV, where D= {(r,y, 2) E R : a s? +y + ...

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Q: Solve the differential equation by using integrating factors. xy' = 3y + x2

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Q: Consider the piecewise function 3.x if x < -2 f(x) = a.x² + 2x + b if – 2 < x Where a and b are cert...

A: Given query is to find the value of a and be.

Q: (a) f(x) = (3x² – 1)/T +x/4 (b) y(x) = r-1 r³+2 (c) g(t) = [(t³ + 4)(t² – 1)]/

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Q: axis. y = 3x2, y = 18x – 6x2

A: Given query is to find the volume of the solid generated.

Q: Consider

A: Please refer to the image below

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Q: Use an appropriate test to determine whether the series given below converges or diverges. 00 In (n ...

A: We have to find if the given series converges or diverges.

Q: 10t2 Suppose the height of an object is given by h(t) = experiment begins. 8t + 3 meters, t seconds ...

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Q: To evaluate the integral 1 dx x2 – 16 2х — we use the partial fraction decomposition of the integran...

A: Explained below

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Q: rove that the given equation is a solution to the given DE: 5. x = 2t + C; y = Ct + 3 ; 2(y')² – xy'...

A: Topic:- application of derivatives

Q: 28. A particle moves along the curve y = 3x2 +1 in such a way that the y value is increasing at the ...

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Q: Find relative extrema for f(x,y)=x^3 - 6xy + 8y^(3) - 2.

A: Question- Find relative extrema for  f(x,y)=x^3 - 6xy + 8y^(3) - 2. 

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A: Let's find. 

Q: yi + yi = 1, when x = 0, y = 4

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Q: Given cost and price (demand) functions C(q) = 100q + 40,000 and p(g) = - 2q + 870, what is the maxi...

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Q: You record the temperature every hour from midnight until​ 8:00a.m. You see that the temperatures​ (...

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Q: Given cost and price (demand) functions C(q) = 100g + 42,000 and p(g) = - 2.1g + 870, what is the ma...

A: Given

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A: Since you have posted multiple questions i can do first question as per our company guidelines pleas...

Q: 4. y = x0sx

A: Take the logarithm then take derivative twice. 

Q: 1. f (х) — 5ӕ -4

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Q: By considering the real and imaginary parts of the product eiθ eiφ prove the standard formulae for c...

A: Given problem:- By considering the real and imaginary parts of the product eiθ eiφ prove the standar...

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A: We have to find the price that can maximize the profit.

Q: 4x 1. Зу': y? %3D

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Q: Consider f(x)=ax+xln(bx)f(x)=ax+xln⁡(bx) for a>0a>0, b>1b>1, and x>1x>1. Find f′(x)f′(x): f′(x)=f′(...

A: f'(x)=a+1+logbx Increasing 

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A: We have to find the solution set for the following equations using guass Jordon method.

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Q: 4. y = 2xi+x“

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Q: Use long division to divide and use the result to factor the dividend completely. (5x2- 3x-14) (x- 2...

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Q: Let S be the sphere of radius 3, centered at the origin, oriented outward. [x³ + 2 sin(z)] y3 – 10xz...

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Q: 1 1 9. dx I (# – 1)(x² + 4x + 5) In |x – 1|+ 10 In a? + 4x + 5| - 20 13 arctan(x + 2) +c 10

A: First we use partial fraction decomposition and then evaluate the integral.

Q: Using f (x) = In(3 – 2x), find the value of L and calculate the radius of convergence of the series....

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Q: Describe the graph of the function. ) (x- 3)2 +7 O parabola opening upward O parabola opening downwa...

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Q: Section 3.7 p. 343/345 # 364 Determine whether the improper integrals converge or diverge. If possib...

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Q: After some thought, you have decided that you will need $60,000 each year to live on after you retir...

A: This is a problem related to simple interest calculation. Based on the general formula of simple int...

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Q: xy²y' = y + 1; y(3e²) = 2

A: Given that a differential equations and we solve this differential equation by using saparation meth...