Given: 4.The trisectrices of maclaurin y²(a + x) = x²(3a - x) Answers: 4. (³x −6x²y² − y )dx+8x³ ydy=0

Q: 8. f(x) = 3tan(x²) e

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Q: Let f(x)=1/x Using the definition of derivative at point f’(a)=lim f(x)-f(a)/x-a f’(3)=lim x->3___…

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Q: Find the inverse transform of the given function of s. F (3)=28+16 2s

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Q: 5. f(x)=e* cos x + e* sin x

A: We use Product rule  ddxuv=udvdx+vdvdx

Q: Eliminate the arbitrary constant y=C₁x + С₂e-2

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Q: The expenditure of a household on consumer goods, C, is related to the household's income, Y, in the…

A: We need to find linear relation.

Q: Let g(x) = (2x − 1)ƒ(*), where ƒ(x) is a differentiable function such that ƒ(2) = 2 and ƒ'(2) = −7.…

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Q: Find an equation of the tangent plane to the given surface at the specified z = y²e*, (0, 5, 25)

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Q: Find the inverse transform of the given function of s. F (s)- A B C D E 1 2s + 16 f(t) = e-8t f(t) =…

A: Given the function: f(s)=1/(2s+16)

Q: Find the indefinite integral. (Use C for the constant of integration.) 2 cos(0) - 1 de

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Q: Can I square the right side of V2r - 1 = r – 2 by first squaring x and then squaring 2?

A: Given data:- 2x-1=x-2

Q: Find the angle between the vectors. (First find an exact expression and then approximate to the…

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Q: 10. What's the standard form of the equation of the following hyperbola? 6 5+ 4 3+ 2+ -6-5-4-3-2-1…

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Q: Assume that functions f and g are differentiable with f(−5)=−2​, f′(−5)=−4​, g(−5)=−5​, g′(−5)=−5.…

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Q: 2 What is the general solution of (x² + 1) dx + x²y²dy = 0 ?

A: Find genral solution of (x^2 +1) dx + x^2y^2 dy = 0

Q: 8. List the set of possible rational zeros for f(x) = x² − 5x³ + 8x² − 20x + 16.

A: List the set of the possible rational zeros for x4-5x3+8x2-20x+16=0

Q: Please identify and sketch the level curves and traces of the curve 4x - y² - 2z = 0.

A: Level curve of function 4x-y2-2z=0

Q: Verifying a Solution In Exercises 5-10, verify that the function is a solution of the differential…

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Q: If f(x) = 3x² - 7x + 6, find f'(-4). Use this to find the equation of the tangent line to the…

A: Given function:- fx=3x2-7x+6

Q: Use the Definition to find an expression for the area under the graph of f as a limit. Do not…

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Q: What is the general solution of xy³ dx + e²² dy = 0 ?

A: First we change the given differential equation into variable separable form then find the general…

Q: Polynomials are added by combining------------------------- terms.

A: To add two or more polynomials, first step is to arrange each polyomial such that the term with the…

Q: Write the product as a sum: 18 cos(35u) cos(12u)

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Q: Solve for the particular solution of y' = 1/1 e 42 +3 sin 2x when x = 0 and y = 1

A: The differential equation is given by y' = 12e4x+3sin2x The initial condition is  y0 = 1 To…

Q: Find all values x = a where the function is discontinuous. For each value of x, give the limit of…

A: The given function is: Px=|x+2|x+2

Q: Find the area of the region that is inside of the cardioid r = 4 + 4cosθ and outside of the circle r…

A: Given: Area of the region that is inside of the cardioid r=4+4cosθ and outside of the circle r=6.

Q: Find the equation of the tangent line to the graph of f(x)=6xln(x+9) at x=3 Answer: y =

A: The given equation is; f(x)=6xln(x+9)  at x=3

Q: 13. Graph the solution set of the system of inequalities: y 8x - 3 O O A. <++++++ -20 10 B. <++++++…

A: Topic- System of inequalities We are given ,y&lt;-x+8 y&gt;8x-3 in slope intercept form , y=mx+c…

Q: 1. P = {(1,4), (-4,5), (2,0), (1,4), (-2,5)} 2. P= {(a,4), (7,3), (2, 3), (,0), (0,5)} 3. R= {(1,a),…

A: Note:- These are multiple subparts questions and according to company guideline we can do first 3…

Q: determine the domain and range of the function

A: Domain: The domain of a function is the collection of all conceivable values that can be used as…

Q: A simplified polynomial that has exactly one term is called a/an…

A: Monomial : A polynomial that has exactly one  term is called monomial.

Q: Consider the curves given by y = x² - 9 and y (A) Sketch the region which included finding…

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Q: (a) Represent the function: x4 - 12x³ + 42x² - 30x + 9 and its successive difference in factorial…

A: The given function is; x4-12x3+42x2-30x+9.

Q: Find the inverse transform of the given function of s. F(s) A f(t)=354-736- 11 B -45²-6 s+4Xs+6XS-7)…

A: A detailed solution is given below.

Q: In Exercises 5-8, find the degree of the polynomial. 5. 3x - 5x + 4 7. x - 4x + 9x – 12r* + 63 6.…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 14. Find y' and y". Be sure to label your work so it is clear which answer is y' and which one is…

A: Let's solve for 1st and 2nd derivative.

Q: How do you know the signs of the derivative at each x-value? How do you know that f'(1)>f'(2)?

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Q: u = (cos())i + (sin())i. Using the limit definition only, find the directional derivative of f(x, y)…

A: The directional derivative at point P(a,b) in the direction of u=(cosθ)i+(sinθ)j is given by…

Q: Apply the law of cosines to the triangle in the accompanying figure to derive the formula for cos (A…

A: Given diagram:-

Q: In Exercises 135-136, list all numbers that must be excluded from the domain of each rational…

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Q: 49 III. Consider the function g(x) whose graph is shown below. The domain and range of g (x) are R…

A: Given

Q: Determining a Solution In Exercises 15-22, determine whether the function is a solution of the…

A: To determine whether the function y=3 cos x, is a solution of the differential equation, y4-16y=0.

Q: What happens if you try substituting 100 for x in 250x 100 - x What does this tell you about the…

A: Given data:- 250x100-x  ?

Q: [x² (9-³) dx 1)-9-² In (9) O 2) +C -9-- 3 In (9) +C 3) 9-³+1 +C 4) -9-³ 9 In(3) +C

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Q: Identify whether the following figure suggest CIRCLE, PARABOLA, ELLIPSE or HYPERBOLA.

A: Here we have to use the basic concept of conic section.

Q: Finding a Particular Solution In Exercises 37-42, verify that the general solution satisfies the…

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Q: The function f(x,y) = 2x + 2y has an absolute maximum value and absolute minimum value subject to…

A: Maximum value is =16/5

Q: For f(x) = 3 + 7x - 19(x^2) + 2(x^4) find the maclaurin series (Taylor series about x =0) Please do…

A: The Solution is given below:

Q: Find the inverse transform of the given function of s. F(3) 6s - 49 s2-8 - 8s +41 A) f B) f f Ⓒ =…

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Q: Determine all values of the constant real number k so that the function f(x) is continuous at x =…

A: Topic:- application of calculus and limit and continuity