Given the polynomial y = 3x³ +21x² +31x + 2, • list the possible rational roots: 2 2 1,-1,-1,- 2,-2, -3, 33 1,−1,

Q: 3. (a) Find the Laplace transform of (i) f(t)=17te-2-3 sin(9t) (ii) fo

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Q: region

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Q: 6.) A function g is defined by g(x)=3e³x, what is g"(2)?

A: Topic = Derivative

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Q: 1. Find the area of the region enclosed by the curves y = x² and y = x by integrating with respect…

A: Please see the below picture for detailed solution.

Q: Calculate Duf( – 4, − 4, 1) in the direction of 7 = f(x, y, z) Round your answer to four decimal…

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Q: (3) Sketch a curve y = f(x) that satisfies: f(0) = 3, and dy dx -2. What is f(x)?

A: The function y=fx that satisfies f0=3, and dydx=-2. We have to find fx and sketch its graph.

Q: Continuing with the same graph of f(x), which value is the greatest: f(5), f'(5), or f(6) -f(5) ?…

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Q: (b) If lim (x,y) →(5,-4) f (x, y) = 1.25, then lim f (x, −x + 1) = 1.25 ? x→5

A: Given limit is limx,y→5,-4fx,y=1.25 We need to verify if limx→5fx,-x+1=1.25 is true using the given…

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Q: Round your final answer to four decimal places. Use linear approximation to estimate the quantity…

A: We knowLinear approximation Lx≈fa+f'ax-a

Q: - Let C be the curve defined by R(t) = (2e²t - 3,1 - e²t, 2e²t). i. Find a vector equation of the…

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Q: 2. Solve the logarithmic equation a) In 10-In(-x) = ln(3-x) b) log₂ (x + 1) = 1 + log₂ (x - 1)

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Q: Exercise 11 = (ƒ(x) + 5.x²)4 Let y = The Chain Rule and suppose that f(-1) = -4 and dy = 3 when…

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Q: Find fx(x,y) and fy(x,y). Then, find fx (2,- 4) and fy (-4,4). f(x,y) = 4x cos (лу) fx(x,y)= (Type…

A: Implicit differentiation is done and then values of x and y are substituted.

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Q: the Wa Salve the... Following.. ......3x³6xy Ax (3x²+2 y.).dy. =a ... ... ... ... ..x 2y.). dy...…

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Q: 2.) What is when y= cos(2x³) d²y dx²

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Q: For the given cost function C(x) = 12100 + 300x + x² find: a) The cost at the production level 1200…

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Q: Selve the following equa 2 Buen DH. ander Re Benze. Xehr...). ....

A: according to bartleby guideline we do only first part      x2dy+(2xy-x+1)dx=0    given equation is…

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Q: Find the equation of the line tangent to the curve 8x4 + 8y² = 16 at the point (1, 1).

A: To find the equation of the line tangent to the curve 8x4+8y2=16 at the point 1, 1.

Q: The following table gives the monthly premiums for an insurance policy on people of various ages. a.…

A: NOTE: Refresh your page if you can't see any equations. . x=age y=monthly premium x y 35 120…

Q: 8.) What is the 20th derivative of y=sin(2x)?

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Q: Graph the following in polar coordinates (a)  3<r<5,    2π/3≤θ≤4π/3  (b)   r=−8sin⁡θ , Label at…

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Q: Q1 Consider the plane curve defined by the parametric equations x = 2 + 2 cos² (t), y = 3+ sin(2t)…

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Q: Let f be the function with derivative given by f'(x) = sin x + cos (2x) - for 0≤x≤. On which of the…

A: NOTE: Refresh your page if you can't see any equations. . the derivative of the function is given by…

Q: 17. sin(x²y²) = x

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Q: Question Let h(x) = f(x)g(x). If ƒ(−6) = 4, ƒ' (−6) = −2, g(−6) = 2, and g'(-6) = 5, what is h'(-6)?…

A: Use product rule of differentiation.

Q: Which of the following is true regarding (2b) given the piecewise function f(x)= Of(2b)=-g(2b)…

A: Please see the below picture for solution.

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Q: Consider the function f (x, y) = = √x² + y² - 4 x - 1

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Q: Suppose that f(x, y) = x³y². The directional derivative of f(x, y) in the direction and at the…

A: To find directional derivative of given function.

Q: Exercise 10 dy Let y = (f(x))³ and suppose that f'(1) = 4 and dx The Chain Rule = 10 for x = 1. Find…

A: We have to find out

Q: 3. Graph the inequality subject to the nonnegative restrictions. Make sure to # the lines…

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Q: Q 5. Solve the following IVP. y" + 3y + 2y = g(t), y(0)=0 y' (0) = -2 2 g(t)= t t<6 6<t<10 t≥ 10

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Q: Solve the differential equation. y' − y = 9ex

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 1.23 Solve each of the following problems by direct integration. a. b. C. d. e. 4x = 3t 5x = 2e-4t…

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Q: Find all of the following for the function y = x¹ ex a. x-intercept(s) b. y-intercept(s) C.…

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