a. y = 3et-2 et +1

Q: Let R be the region in the first quadrant bounded by x^2 +y^2 =4, y^2 = -x+4 and y=0. Set up the…

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Q: If u and are orthogonal to each other, then u x O True False = 0.

A: Given :u→ and v→ are orthogonal

Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: Given problem:-

Q: Find the general and Singular Solution of the Following differential equation y²Lny = xyP+ P²

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Q: Analyze and sketch the following curves.Indicate the intercepts, asymptotes, and critical points

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Q: Tiffany has the following coins in her piggybank a 1cent, 5cent, 10cent, 25cent, 1 dollar and 2…

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Q: Solve it neatly, correctly, and comprehensively.  2. An open box is made from a thin sheet of…

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Q: f(x) = x²+3x x+3 "2"⁰ 24

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 1. d²y dy +6- dt² dt +8y=-4 cos(3t)

A: We need to solve D.E. As per Bartleby's guidelines we can solve one question from multiple question.…

Q: In 7 + 4√3 2.63391 ≈

A: The given expression is  ln7+43

Q: 1 If sin(0) and is in the 4th quadrant, find cos(0) 8 cos(0) = Enter your answer as a reduced…

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Q: The integral of sin x³ dx is cos x + Option 1 cos³ x 3 + C cos x + Option 2 cos² x 2 + C

A: Given ∫(sinx)3dx=∫sin3xdx

Q: Use triple integration in Cartesian coordinates to find the volume of the region in the first octant…

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Q: 5. Find parametric equations for the line through the points (1, 3, 0) and (2, 4, 4).

A: The line passing through the points 1,3,0 and 2,4,4

Q: Use integration by parts to find the integral. (7x-3) e-2x dx -2x dx = (7x-3) e

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Q: The function defined by y=√√²-x² has as its graph a semicircle of radius r with center at (0,0) (as…

A: The objective is to find the volume .

Q: Write an expression for the new function when g(x) = 3 + 8x is translated / shifted one (1) unit…

A: Given problem:- Write an expression for the new function when g(x) = 3 + 8x is translated / shifted…

Q: 6.) I. Simplify. Write "undefined" for expressions that are undefin -3 -6 -2 6 619 1 4 -4 -4

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Q: Determine the scaler equation of the plane with × -intercept=2, y intercept=-1 and z intercept=3

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Q: 8x²-x+8 x(x² + 4) 2 lnx + 6 in (x²+4)-4 Arctan ¹ (1) + C Option 1 4 Inx+6 In (x²+4)- Arctan (+C…

A: topic -indefinite integral

Q: 7) Use the double integral of a cross product to find the surface area of x = z² + y that lies…

A: Let's find surface area  by using double integral.

Q: 4. Find an equation for the plane through (1, 3, 4), (2, 2, 3), and (3, 2, 1).

A: Given problem:- 4. Find an equation for the plane through (1, 3, 4), (2, 2, 3), and (3, 2, 1).

Q: The given integral is equal to cos 3t dt 5 + 3 sin 3t O (1/3) In 15 + 3 sin 3t| + C O (1/9) In 15 +…

A: To find out the integration.

Q: 1 If sin(0) and is in the 4th quadrant, find cos(0) - 8 cos(0) = Enter your answer as a reduced…

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Q: Given f(x) = x-1 2 on [- 2, 2]. x²+1 a. Find the critical numbers of f on the given interval. b.…

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Q: Which of the following graphs is the correct plot of y = 5+ 5 4 4 -3 3 2 2 -1 + 5 6 2 4 -1 -2 --3-…

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Q: Calculate the area contained between the curve y = cos x,-<x<, and the line y = 1/2. T 3 √3 Option 1…

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Q: The region R is bounded by y = √x and y = x³ is revolved about the y-axis. Find the volume of the…

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Q: Ice O 3.19 O 13.9 O 12.6 O 16.1 O none of the above (ezt - e-²t)² dt

A: Given that a integration and we solve this integration by using general formula of integration. Here…

Q: Given f(x,y) = 6x^2 - 2x^3 + 3y^2 + 6xy. Determine any local maxima, local minima, and saddle…

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Q: Find the general solution of the following DE. xy² (y')² + y(x - 1)y' - x³ = 0

A: The given differential equation,    xy2y'2+yx4-1y'-x3=0

Q: Solve using Variation of Parameters (D² + 1) y = tan x O y = c₁ cos x + c₂ sin x − cos x ln(secx +…

A: The objective is to find the general solution using variation of parameter.

Q: 2x² + x + 3 x³ + x dx In[x] + In (x² + 1) + tan^³(x) + C Option 1 3 In]x] +In (x² + 1) + tan¹(x) + C…

A:

Q: Find the area of the region bounded by y = x³ - 8 the x-axis and the y axis. 1/3 3 1/9 9 None of the…

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Q: Convert the Cartesian coordinate (-2,-4) to polar coordinates, 0≤ 0 0 r = Enter exact value. 0 =

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Q: What is the general solution of the following ODE * (x² + xy − y²)dx + (²x² − 2xy) dy = 0 1 1 x³ +…

A: We know that the equation is of the form of  Mdx+ Ndy = 0  We will check whether the equation is…

Q: √ /1 + x² dx

A: We can solve the integration as below.

Q: 3. y= x²-3x-4 x+2

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Q: Let f be a twice differentiable function on an open interval (a, b). Which statements regarding the…

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Q: r(x) = 5 log4 (3x + 10)

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Q: F=x²y³z¹i-xyzj+(x+y+z)k

A: The vector field is F→=x2y3z4i^-xyzj^+(x+y+z)k^

Q: 6. If If vectors (5,2,-1) × (2,-1, a) = (5,-12,-9) then determine the value of a.

A: Given: 5,2,-1×2,-1,a=5,-12,-9

Q: Determine the volume produced by the region bordered by 32 IT 15 "1 x² - 4x - 4y + 4 = 0 and y = 1…

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Q: dx | | dt dy dt dz dt = 3x + 2y + 4z = 2x + 2z = 4x + 2y + 3z

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Q: 5TT Without using a calculator, compute the sine and cosine of 6 What is the reference angle? In…

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Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x² + y² + z² = 1 is…

A: Let's find lowest and highest temperature by using langrange multipliers.

Q: II. Find the inverse of each matrix. 5 -11 1. -7 -9

A: A-1 =1AadjA .

Q: Find the indefinite integral. (16x +13) In (2x)dx Select the method of integration that should be…

A: Integration by parts ∫udv=uv-∫vdu

Q: Convert the rectangular coordinates (5,-5√3) to polar form. Letr> 0and 0 <0<2TT.

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Q: क्ने Find the curl of F(x, y, 2) = (2x,3y, 52). depends on the point (x, y, z) ● 10 O

A: Let's find curl.