Find the total area bounded by the graphs of f(x) = 3x³x² - 10x and g(x) = -x²+2x. O 32 units² O 8 units² O 12 units² O 24 units2

Q: Find the particular solution of each of the following. (4+sine)y'=e*(6soc² e* - ycose); y(ln x) =…

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Q: e correct answer below. , because f(x) has a limit as x approaches c if and only if and only if it…

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Q: Find the area bounded by the curves x y = 8 (in green), y blue) and the line 3y sliced pizza? 2 =…

A: Let's find area of the sliced pizza.

Q: What is a suitable integrating factor that can be used to solve the equation dy +2y-4xy-e* cos(2x) =…

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Q: 8. Find the limit of f(x) = lim f(x)= 4- 818 (Type a simplified fraction.) lim f(x) = 8118 (Type a…

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Q: Which among the choices is the same as the differential equation dP dt = = P(C₁-C₂P)?

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Q: The linear trend forecasting equation for an annual time series containing 45 values (from 1963 to…

A: Given     Yi^ = 4.8 + 1.3Xi As per the student's request, I am providing the solution to the (c)…

Q: 4. Find the limit. lim x-0 lim X-0 5+5x+ sin x 6 cos x 5+ 5x + sin x 6 cos x CA. Yes, lim f(x)…

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Q: Solve for the value of C in the equation: +ycotx OA. -5 O B. 5 C.-4 O D. 4 dy dx E. None of the…

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Q: The degree of homogeneity of the function ƒ (x, y) = (x² − 4y²)−¹/² A. 1 B.-1 C. -1/2 D. None of the…

A: The given function is fx,y=x2-4y2-12 We have to find the degree of the homogeneity.

Q: Obtain the differential equation whose general solution is y = C₁ + c₂e³x₁

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Q: a -- In words, describe the curve F(t) = (2 sint,e',2 cost) for 0<= t <=6 . Be sure to give enough…

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Q: Find the 2nd derivative F(x) = 5e^2x F(x)= 3e^-x + 2e^4x

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Q: Which of the following is NOT true about the linearity of differential equations? O A. Which of the…

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Q: (d) Let y(x) = [tan-¹ (√)]4. Find y'.

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Q: The partial fraction decomposition of f(x) X - 5 + g(x) x + 5' where 56 x² - 25 can be written in…

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Q: (5) Find the center of mass of the region bounded by y = sin x between x = 0 and x = 7 above the…

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Q: Evaluate the following integral. π/4 S 0 cos x)² dx secx+cOS X)

A: Explanation of the answer is as follows

Q: If ƒ(x) = 8x¹¹(»), find f'(8).

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Q: If f(x) f'(x)= -3x sin²(x) + 3x cos² (x) + 3 cos(x) sin(x) = 3x sin x cos x, find Find f'(4) =

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Q: write law of cosines.

A: Cosine rule:- The Cosine Rule says that the square of the length of any side of a given triangle is…

Q: If F(x) = f(g(x)), where f(-3) = 5, f'(-3) = 2, f'(1) = 3, g(1) = -3, and g'(1) = 5, find F'(1).…

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Q: 5. Logarithmic Differentiation Method dy (a) Let y = x. Compute by using logarithmic…

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Q: 4. Let sin² x + cos² y = x² + y². Find y' by using implicit differentiation. ។

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Q: Question 9 Which of the following equations has a solution of the form F(x,y) = C A. 2x + 3y + (2y +…

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Q: Solve for the value of C in the equation: (3xy² + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2 OA. 4 OB.…

A: To find the value of C

Q: Solve for the value of C in the equation: dy − (y + xy5)dx = 0 when y(0) = 1 - A. 1/4 B. 1/2 C. 3/4…

A: Find integration factor first as it is linear differential equation

Q: If f(x, y) = 64 - 8x² - y², find fx(1, 2) and fy(1, 2) and interpret these numbers as slopes. fx(1,…

A: F(x,y)= 64 -8x^2 - y^2

Q: X lim x0√1 + 8x - 1 ||

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Q: 6. Let f(x) = 4x² - x + 2 √x Find the equation of the tangent line (in the form y = mx + b) at x = 1…

A: To find the tangent line.

Q: cost function for Joanne's T-shirt production. hirts must she produce and sell in order to break…

A: we will find the required.

Q: Solve the initial value problem y' ○ In (y) + In (1+x²) = ln (2) ○ In (y) = In (1+x²) + ln (2)…

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Q: The Cartesian coordinates of a point are given. (a) (b) (4,-4) (i) Find polar coordinates (r, 0) of…

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Q: Which of the following is a non-homogeneous function? O O tan³y/x | xLnx − xlny x³ - xy + y² (y² +…

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Q: 11. Define what it means to say that lim g(x) = k. the motion y X-0 Choose the true statement below.…

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Q: Solve for the value of C in the equation: (3xy² + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2 O A 4 OB.…

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Q: b = PQ Given the vectors a = (2,-1, 3), P(1,1,1) and Q (5,1,-1) and Z = T J + 3R Where ● Find the…

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Q: Find the limit of each of the following sequences, using L'Hopital's rule when appropriate. √n Vn+1

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Q: 7. Find (a) the slope of the c y=9x² -1; P(4,143) (a) The slope of the curve (Type an integer or a…

A: solution:-y=9x2-1slope= dydx=ddx9x2-1=18x(a)slope of tangent at point P(4, 143)slope = 18(4)=72

Q: g(t) = -tan² (2+) +sin (3+¹+8+³) [[// (++1)]] cot " (cosh (3+1)), ift 71 if t <0 ifo≤t≤1

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Q: Solve for the value of constant C in the equation: (2x + 3)y' = y + (2x + 3)¹/² when x = -1 and y =…

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Q: Find the present value of $4000 payable at the end of 4 years, if money may be invested at 8% with…

A: The amount $4000 payable at the end of 4 years, the money invested at 8% with interest compounded…

Q: A chemical substance has a decay rate of 6.9% per day. The rate of change of an amount N of the…

A: Given :- dNdt=-0.069N

Q: 23. The accompanying figure shows the graph of y = -x² shifted to two new positions. Write equations…

A: Given: The figure shows the graph of y=-x2 shifted to two new positions. To write the equations of…

Q: b) Find the area of the region described. The region inside the rose r = 2a cos 2β and outside the…

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Q: Evaluate the following integral using trigonometric substitution. x² 441-x² S dx

A: ∫x2441-x2dx

Q: f(x)=4ln(4x+6ln(x)), find f'(x).   f'(x)=

A: Given query is to find the derivative of the function using chain rule.

Q: A distribution of values is normal with a mean of 22.3 and a standard deviation of 41.1. Find the…

A: Given that a distribution of values is normal with a mean of 22.3 and a standard deviation of 41.1 .

Q: Let f(x) = 4x + 4 6x + 7 Determine (fof)(x).

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: The integrating factor (IF) of the equation y' - 2ycot2x A. sin2x B. cot2x C. Lnsin2x D.csc2x None…

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