at L'Hôpital's rule may not apply or may require multipl w and, if necessary, fill in the answer box to complete yo in simplified form.) t

Q: Let f(x, y) = ln(x + y − 1). Then, ƒ(e, 1) =

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Q: Find the general solution of the following differential equation. y" 6y + 11y = 0 - NOTE: Use c₁ and…

A: This question is based on solution of Complementary function of diffrential equation.

Q: Evaluate the following double integral by converting to polar coordinates where J 5xy 2x² + 2y² R…

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Q: 5. Find the exact value of distance from the point (1, -3, -1) to the plane 2x-y+3z = -5

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Q: B: Draw the function y = √√x-8

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Q: Find fæxyzz for f(x, y, z) = z³y² ln(x). [Show your solution.] Select one: O O O x² 6z²y x² 2z³y x²…

A: See this solution in below.

Q: In 1991, there were 41,628 shopping centers in a certain country. In 2001, there were 48,434. (a)…

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Q: 1 (√x² – 9) , -dx

A: ∫vn dv =vn+1n+1+C .

Q: X The variable h is the height of the ladder's top at time t, and x is the distance from the wall to…

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Q: Refer to the figure and find the volume generated by rotating the given region about the specified…

A: We have to find the volume generated by rotating the region

Q: Assume that the radius r of a sphere is expanding at a rate of 70 cm/min. The volume of a sphere is…

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Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

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Q: Solve the following differential equation Ỳ – (sinx) y = 2 sinx

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Q: An object is dropped from 260 ft. above the surface of the moon with an initial velocity of 0…

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Q: Evaluate √t (3t-t²) dt

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Q: Use the graph to find the following limits. a. lim f(x) b. lim f(x) X-3 X→-1 a. Find lim f(x) or…

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Q: Both Trapezoidal Rule and Simpson's Rule give the same result when applied to any polynomial of…

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Q: f(x) = 6x3 - 9x + 4 +4

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Q: Find the volume, in cubic units, generated by revolving about the x-axis the area bounded by the…

A: Solution is given below:

Q: The first step in computing the area of regions using the limit definition is to write the given as…

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Q: Find the general solution of the following differential equation. y" + 12y' + 37y = 0 NOTE: Use C₁,…

A: We have to find the general solution of the differential equation y''+12y'+37y=0.

Q: The base of a three-dimensional figure is bound by the circle x² + y² = 9. Vertical cross sections…

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Q: 9. y = logs (e cos(2x))

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Q: Q2) Find the area of the surface generated by revolving the curve y=√4-x² about y-axis.

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Q: a-limx-4(2)

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Q: - If u = 4j – 2k and v = 27 − j + 7k, find || − 3ủ + 5v||. Select one: O 2√230 O 3√373 O 2√373 O…

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Q: A population of a small city had 3000 people in the year 2000 and has grown at a rate proportional…

A: In this question, we will use growth topic of differential equations.

Q: The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving…

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Q: 65. Find the volume of the solid formed by revolving the region bounded by the graphs of y = 3-x²…

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Q: 1. Evaluate the iterated integral. (a) */2 sin 8 IT 00 */2 asine (b) ² dr de 0 rcos 0 dr de 0

A: A.

Q: x² - xy (x,y) (0,0) √√√√y If it exists, find lim Answer: .Write DNE of the limit does not exist.

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Q: 12. R sed e A fourth-degree polynomial P(x) satisfies A4P(0) AP(x) = P(x + 1) - P(x). Compute…

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Q: P/ find the slope and y-interceft of the line. 8x+59=20

A: In this question we have to find the slope and y-intercept of the line.

Q: * The Simpson's Rule gives the exact result when applied to any polynomial .of degree-➖➖➖➖➖➖➖or less…

A: Simpson's Rule: It is a numerical method for approximating the integral of a function between two…

Q: IF B = By using the result of det(A) (A) Find the value of det(B) (B) without use the def (det) if…

A: Let's find determinant of given matrix.

Q: The solution of differential equation y' + (cot x) y = 3 sin x cos x, x = (0,π). is:

A: Using Integrating Factor formula:

Q: A Let R be the region bounded by y = √cos x, x = generated when R is revolved about the x-axis. 4'…

A: Follow the procedure given below.

Q: Evaluate the following antiderivatives. f (x sinh x + 1) dx

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Q: 59. A. If ey dy = 3x² and y(1) = 2, then the particular solution y(x) is dx y = ln x³ +2 C. y = ln…

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Q: Q ssosiee ※ dy nolaeV DOY MEMedua s x24

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Q: Write the parametric equations for the given vector equation: [2 [x, y, z] = [11,2,0] + t[3,0,0]

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Q: Problem 4: Find the derivative (f'(x)) of a) f(x) = (x² − 3x)(7x+15), b) f(x) = = x-5 x²-x+7

A: Given f(x)=(x2-3x)(7x+15)DIfferentiate…

Q: Compute TOT/ cos(y³) dydx. [Hint: Change the order of the integration.] Show your solution. Select…

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Q: Determine the slope of the tangent line to the curve y=2 – x2 at the point (3,-7)

A: slope of tangent = slope of given curve  step 1  we have to find slope of curve  slope = dy/dx  so…

Q: 1. An object starts from rest at point P(1, 2, 0) and moves with an acceleration of a(t) = 3 + 2k.…

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Q: 1. Prove Trigonometric Identity (a) cos (sec) - cos 0) = sin2 0 cose (b) (c) 1-sin 0 1+cos 0 cose =…

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Q: Find the absolute extremum, if any, for the following function. f(x) = 4x+ -7

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Q: A conical tank has height 3 m and radius 2 m at the base. Water flows in at a rate of 2 m³/min. 3…

A: Given: Rate of inflow of water, dVdt=2 m3/min Height, h= 3m Radius, r=2m

Q: The approximated value of the integral fe* dx is equal to - Rule with step size (h=2). when using…

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Q: 8. Given the space curve r(t) = (sin²t, cos't, tant), find an equation of the tangent line in…

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