Examine the following functions for maxima-minima and trace the curve a. Y=x* + 1 a?x b. Y= a² –x²

Q: In the following questions, determine the 7x3 + 9x behavior of h(x) – x³ + 10x If a limit does not e...

A: Given query is to find whwrw fui is undefined , vertical asymptot and hole.

Q: Evaluate the integral. | cos" (x)dx cos"(x)dx

A: According to question,given Integral,Let I = ∫ cos-1x dx

Q: An open-box with a square base is to have a volume of 500 cubic inches. The material for the top and...

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Q: (b) Given the first-order differential equation as below: (x² +3y² +5)dx+(6xy +6y+3)dy = 0 (i) Ident...

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Q: Expand the expression. If possible, write your answer without exponer x² - 5 log 5 3+x2 2-5 log 5 3+...

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Q: Live equation ar differential with constat coefficients dx -3x 3x = -9ゼー1 5. | dt? dt

A: We have to find the general solution of differential equation

Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for th...

A: Given problem

Q: Since the start of the year, the price of gasoline has been decreasing at the cost of 5 cents per ga...

A: We  have given that the start of the year, the price of gasoline has been decreasing at the cost of ...

Q: Given an ordinary differential equation in the form: (xy + y² + y)dx – (x + 2y)dy = 0 (Eq. Test the ...

A: According to question,Given Differential equation,xy + y2 + y dx - x + 2y dy = 0

Q: Explain why the Intermediate Value Theorem is not necess arily guaranteed fo f (x) = = CSC for x E (...

A: Topic = Functions   The intermediate value theorem states that if f is a continuous function whose d...

Q: (a) Show that if (a,342) = 171 and (b, 342) = 171 then (a+b,342) = 342. %3D %3D (b) Show that if (a,...

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Q: (sin x – 1) dx + (cos x + 1) dх %— 0. D.) - (1+) А.) —89 C.)- 1 В.) —91

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Q: The given problems need the first derivative. Find the first derivative. y = 3x + 6 y = x2 –1

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Q: Write each of the given numbers in the form a + bi : (a) e- i, e(1+i27) (b) el-1+) i, (c) ee i.

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Q: dx What should be the rewrite of the integrand of f so that the resulting integral is integrable? 1+...

A: We have to find integrand 

Q: Given the first-order differential equation as below: (x² +3y² +5)dx +(6xy + 6y + 3)dy = 0 (i) Ident...

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Q: dy (x + 1)+ (x + 2)y = 0 dx Both C and B Integrating Factor - First order Leaner Separable method Ex...

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Q: How many transformations must be applied to the graph of the function f(x) to get the graph of the f...

A: The transformation from f(x) to g(x)=2f(2-x)+2

Q: A ball is thrown straight up into the air off the top of a building so that is height in feet after ...

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Q: L:(sin x – 1) dx + ,cos x + 1) dx =? c)-1 а.) -89 b.) -91 d.) - (1 +)

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Q: xy* Let f (x, y) = if (x, y) # (0,0) and f (0,0) = 0. (a4+6y8)

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Q: Find the center of mass of a thin plate of covering the region between the x-axis and the curve y = ...

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Q: 19. Find the total area between the parabola y = x² - 4x, the x-axis, and the ordinates x = -2 and x...

A: To determine:

Q: 59. Biophysics. In biophysics, the equation (L + m)(V+ n) = k is called the fundamental equation of ...

A: Given, (L+m)(V+n)=k Formula: d/dx (uv) =u(dv/dx)+v(du/dx)  

Q: The distance d of a particle moving in a straight line is given by d(t) = 2t3 + 5t – 2, where t is g...

A: Note that:-Velocity of a particle is given by differentiating distance d(t) with respect to (w.r.t) ...

Q: ghing 16 pounds stretches a spring feet. The mass is initially released from rest from a point 2 fee...

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Q: 15. A particle moves along a straight line and has acceleration given by s" (t) = 5t + 3. Its initia...

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Q: 3. Find the indicated values. a) f(x) = x³, g(x) = 6. (f°g)(x)? b) f(x) = -2x + 1, g(x) = x², h(x) x...

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Q: Find numbers a and b, or k, so that f is continuous at every point. 3x+ 9, if x<-6 f(x) = { kx+ 6, i...

A: Hair we are given that the function is continuous at every point. we use the concept of limit for fi...

Q: 30A ball is thrown straight up into the air off the top of a building so that is height in feet afte...

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Q: LINEAR DIFFERENTIAL EOQUATION WITH CONSTANT COEFFICIENT (STEP BY STEP SOLUTION) d2x dx 3x = -9t² – 1...

A: The given differential equation is; 2d2x/dt2 - 5dx/dt -3x =-9t2-1. t=0,x=1,dx/dt=0.

Q: A population of bacteria has 1175 bacteria in its starting population. The half-ife of this particul...

A: Given:   Bacteria : 1175     Days : 14

Q: 3. (D5- D-2D3 + 2D2 +D – 1)y = 0

A: This is a differential equation problem

Q: Written Work Directions: Please write your solution on the space provided and boxed your final answe...

A: limit

Q: Solve the differential equation y' = e4Y sin(5x) and choose the correct answer from the following op...

A: Given:- y'=e4y sin(5x)  To find:- General solution of given differential equation

Q: 4. Determine if the relations given by the graphs below give y as a function of x. If so, determine ...

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Q: Given: G(x) = [x] + [4 – x]. Determine lim G(x). x-3

A: We will find the limit of the given function.Below find the solution in the image.

Q: 11. Find the total area between the parabola y = x² – 4x, the x-axis, and the ordinates x = -2 & x =...

A: Here we have to find the total area between the parabola y=x2-4x, the x-axis and the ordinate x=-2 a...

Q: b. Let g(x) = x² – 7. Determine the root(s) of g. 7,-7 Preview 7 = 7., – 7 = -7. c. Let h(x) 5x? - 3...

A: Topic = Algebra

Q: Solve the given linear differential equation with constant coefficients. Solve each and show complet...

A: Please see the below picture for detailed solution. 

Q: An object is shot upwards from ground level with an initial velocity of 3 meters per second; it is s...

A: Use energy conservation equation.

Q: Consider the graph of f. y 4 3 1 1 2 2 3 4 5 6 7 8 9

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Q: Find the area enclosed by the x-axis and the curve y = -x² + 9. 32 A.) s.u. B.) 18 s.u. C.) 36 s.u. ...

A: Follow the procedure given below.

Q: (D2+ 4D +5)× = 13e3t+ 5ot

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Q: Given a function whose graph is shown below. 1 0.5 -5 -4 1 2 -0.5사 -1.5 Determine lim f(x). r--1

A: We have the find the limit of f(x) at x = -1 using the graph of f(x).

Q: (e* –1) -dx (e +1) vel

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Q: Evaluate f*27 dx. x+3 A.) + 9x + C B.) 3 3x2 + 9x + C 3x2 C.) 9x + C 2 3x2 D.) ++9x + C I + +

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Q: The definite integral (-+) dx when evaluated is equal to - 11 Find the value of a." 12 3Vx. a

A: Given ∫49-xa+13xdx = -1112we know that∫xn dx = xn+1n+1 + C

Q: dif ferential equations I. (3x-y- 4) dy =( x +y -4) dx when X-3 y-1

A: As per company guidelines we can solve first question. I hope that the given solution will help you....

Q: Select the function that would represent g.

A: