Calculate the integral approximation S6 for 0 -1 4-² dx.

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A: Given; f(x)=maxi .xi

Q: In problems 5 and 6 find the particular solutions of the given differential equations. d²y dy +9y =…

A: To find the solution of the given differential equation.

Q: Find lim f(x) and lim f(x) for the given function and value of c. f(x)=(x+4) |x+31 X+3 C-3 lim (x+4)…

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Q: Sand is pouring out of a pipe and is forming a conical pile on the ground. The radius of the pile is…

A: Given:-radius of the pile  is increasing at a rate of 4 ft/daydrdt=4 ft/dayheight of the pile is…

Q: y=-x v-3x³ x32 has starting point A whose x-coordinate is 3. Find the x-coordinate of The curve the…

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Q: Q6: Find the Fourier coefficients and Fourier series of the function f(x) defined by -HAXNO f(x) = 0…

A: Here, the given piecewise function is: f(x)=0; -π<x<0x; 0<x<π and the period L=2π

Q: f sinh3³ x dx Ocosh³z-coshz+C O3 cosh³r+C 3 Ocosh³z + cosh 2+ C Ocosh³ +C O None of the choices

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Q: Find the limit. x² - 25 lim x 5 x²8x + 15

A: We need to find the limit:limx→5x2-25x2-8x+25

Q: A. Determine whether each integral is improper. If it is improper, give your justification. 1. ft x²…

A: The given integral is improper. An improper integral is a definite integral in which the integral is…

Q: The graph of a rational function, f(x), has a point of discontinuity when x = 2 and an asymptote…

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Q: 5- prove that - for sin Ꮎ dᎾ cose Ꮎ dᎾ

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Q: Calculus optimisation problem Amount of fuel 'F' (in litres) required per hour to propell his…

A: Given, F(u) is the fuel in liters required per hour. u is the speed in kn/hr u(max)= 40 km/hr F(u)=…

Q: Solve the following equations by using Cramer's Rule 2x + 2y + z = 1 x-y + 6z = 21 3x - 2y-z = 4

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Q: 8.A kite at an altitude of 200 ft. moves horizontally at the rate of 20 ft/sec. At what rate is the…

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Q: Evaluate the iterated double integral √1-x² _L [ ³²-x² sin (x² + y²) dz dy dx

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Q: The total amount of money in circulation for the years 1990-2012 can be closely approximated by…

A: This question is related to rate of change, we will solve it using given information.

Q: The solution interval of 2y +1≥3 or 3y1 or y< -11 BO

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Q: Which of the following is the formula for the length of the arc, L, of the curve y = f(x) such that…

A: The answer is given below:

Q: LAW OF GROWTH AND DECAY A bacteria culture increased 800% in 1 year. How long (in months) will it…

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Q: ∞ Find the interval of convergence for n=1 The interval of convergence is a E (x − 4)" n² 3n

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Q: π Determine the slope of the tangent line, then find the equation of the tangent line at t = 4 x = 9…

A: Topic = Derivative

Q: Consider the function 2x+6 f(x)= x²+6 Find the critical point(s) off. (Give yourans wer in the form…

A: f(x) =(2x+6)/(x2+6)  Find:- Critical points  Local maximum and minimum at x= Interval function…

Q: B. Determine whether the following definite integrals converge or diverge and evaluate each…

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Q: B. Find all the values of x on the open interval (-5,5) where g is increasing. Justify your…

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Q: Find the marginal profit function if cost and revenue are Pix- given by C(x)=215 +0.7x and R(x) = 3x…

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Q: [f(a)]² =

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Q: Using polar coordinates, evaluate the integral sin(x² + y²)dA where R is the region 1 ≤ x² + y² ≤…

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Q: II. Solve the following problems. Enclose final answer. 10. At what rate is the vertex angle of a…

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Q: 2) 1 Vl-x dx

A:

Q: Evaluate the iterated double integral 2.) S S ₁² x y e² dxdy 2 b.) ^ S = sinTy³ dydx JI-X² c.) ["…

A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: We are interested in the first few Taylor Polynomials for the function f(x)= 7e + 3e-* centered at a…

A:

Q: What is the volume of the solid generated by the area bounded by y=x² and x=y², and revolved about…

A: Given curves y=x^2 and x=y^2

Q: II. Solve the following problems. Enclose final answer. 10. At what rate is the vertex angle of a…

A:

Q: Find the gradient of f(x,y,z) = (x² + y² + z²) Vfl (1,2,2)=(i+₁+O (Type integers or simplified…

A:

Q: Given [ƒ(x) dx = -5, and g(x)= {x²-1,0≤x≤3 . Using the properties of (3x+2 ,3≤x≤5 integral. Find the…

A: Ans= -20  For detail...go through the solution...I have solved using given information in detail

Q: a/ Q ((Laplace)) 1 A²² [5 (5²+25+5)]

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Q: Integrate the given series expansion of f term-by-term from zero to x to obtain the corresponding…

A: We have to find the series.

Q: Given ~ √x³ √4-x² dx. Ⓒ-² (4-2²) dz Ⓒ√2 (4-2) 1/² d Ⓒ/(x++4+²) dz Ⓒ -√2² (4-2²) ³/2 dz dx. If we let…

A: topic- indefinite integral

Q: 8. 位 dx √x

A:

Q: 4. Given z = x-y x+y Find əz/ax

A: I have appended the formula used in the solution part of the question.

Q: Write an equivalent expression using exponential notation: a3

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Q: The value of f (3), for the following function f (x)=√√2x-20

A:

Q: 5 √₁ (2x² - 2. 2 (2x² – 3x) dx

A: We can solve the definite integration as below.

Q: Determine the amplitude, period, and phase shift for the given function. y = 1 cos 2x - cos(2x - 3)…

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Q: 2. The Minimum point of y= 8x+4 (x-2)²

A: To find the minimum point of y=8x+4x-22.

Q: 2 1) x² + y² + 18x - 26y+246=0 CX+972+(₂-137² = 4

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: Given a -5, b=8, and the angle between them 150º, find: ) the magnitude of the vector a +b ) the…

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Q: Using any of the methods discussed for both numerical differentiation and numerical integration…

A: answer is in next step.

Q: The range of the function f (x)=6x-8 is all integers numbers. صواب

A: Here, the given statement is: The range of the function f(x)=6x-8 is all the integer numbers.

Q: 2e^xdx-3e^ydy=0   What is y'? What is its integral?

A: