Evaluate the integral by converting to polar coordinates. 3 S³ S 0 9-x² cos(x² + y²) dy dx = 0

Q: The function f (x, y) = x³ - 3x² y + 3xy²-y3-11 22-2xy +49 y2 - 16 x + 208 y + 131 has a critical…

A: In this question, we will solve the all parts.

Q: f(x) = x³ - 27x + 8

A: f(x)=x3−27x+8

Q: Let Compute dw (-5,-2)= -(-5,-2)= ow Ət w = xy + yz - 5xz, x = st, y = est, z = ²

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Q: What is the volume if a 6 inch square is cut out

A: Consider the box

Q: SYSTEM: x + y + z = 6 2x - y + z = 3 3x z = 0 -

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Q: Describe the x-values at which f is differentiable. (Enter your answer using interval notation.) X…

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Q: 2) Draw a direction field for the given differential equation. Based on the direction field,…

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Q: Consider the function f(x) = -2x³ + 36x² - 192x + 1.

A: f(x)=−2x3+36x2−192x+1

Q: Evaluate the double integral over the given region R. (18y² - 10x)dA R: 0≤x≤4, 0≤y≤3 R SS (18y² -…

A: evaluate the double integral over the given region  R: 0   0

Q: Suppose that P(t) (with t in months), the fish population in a lake contaminated by chemicals,…

A: Given Differential equation as follows

Q: Seperate the variables and solve the equation (dy/dx)=-e^(x-y). Use the initial condition x=0; y=0…

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Q: Find a general solution of the differential equation 2 dy dx You may leave the solution in implicit…

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Q: use implicit differentiation to find dz/dx, where it is defined, if ln(x^2+y^2+xz)=5

A: The given equation  is

Q: Use Substitution method 4x - 3y = 5 x + 2y = 4

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: (a) Find parametric equations for the line segment that joins the point P(2, 3, -3) to the point…

A: To find the parametric equations for the line segment that joins the point .Note: Since the student…

Q: Solve the exact initial value problem 3y² dx + + (³1²575 2²2 + √²4) · + √2y) dy = 0, y(0) = 2, y5 X…

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Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.01 cm/min.…

A: Radius = 60cmdr/dt = 0.01 cm/min.

Q: 6. Logarithmic differentiation Use logarithmic differentiation to evaluate f'(x). f(x)=(1+x²)in x

A: The given function .The aim is to find the derivative of the function using the logarthim…

Q: ROBLEM No. 1. Solve the IVP: y"+6y-7y=0, subject to the initial conditions: y(0)=5; y '(0)= -3.

A: Given Differential equation is as follows

Q: 7. Given F(x)=√√√x+3 A. Find (fo (fog)(x) B. Find (9°F) (2) gof) → g (x) X -2 report domain and…

A: f(x)=sqrt(x+3)g(x)=x2-2.

Q: S Write an equation for a line parallel to y y = -4x + 4 and passing through the point (4,-2

A: To find the equation of a line parallel to y=−4x+4 and passing through the point (4, -21), you can…

Q: e,f,g

A: By using previous solution sign Table xf'(x)Positive zeroNegativeDNENegativezeroPositive

Q: Use Rolle's Theorem and a proof by contradiction to show that the function f(x) = 6x³ + 4x - 11 does…

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Q: Evaluate the following limit. lim 8+←8 15 ln x X = Note: Input DNE, infinity, and -infinity for does…

A: Given,

Q: Seperate the variable and solve the equation 2y (dy/dx) + 2x = 0. Use the initial condition x = 0;…

A: The given equation .The aim is to find the solution with the initial value .

Q: Find the absolute maximum and absolute minimum values of f on the given interval. π [7] 0, 2 f(t)= 2…

A: In this question, we will find the absolute maximum and minimum values.

Q: Find the critical numbers and the open intervals on which the function is increasing or decreasing.…

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: Assume that  are both  differentiable  functions of t.(a) To find , given that (b)  To find , given…

Q: For which values of x are the vectors (2x, 4, x) and (-1, -2, x) orthogonal? Select one: O None of…

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Q: Evaluate the following integral, (9x - y²)dx + xy dy where C is given by x X = 5t, y = √t, 0 ≤ t s…

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Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

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Q: Air Traffic Control An airplane flying at an altitude of 6 miles passes directly over a radar…

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Q: Find the surface area of the surface given by the portion of the paraboloid z=x^2+y^2  that lies…

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Q: TO Find the length of the curve y = In (2 sec x) for 0 ≤x≤ xs 6 The arc length of the curve is (Type…

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Q: Find an equation of the tangent line to the curve at each given point. x=2-3 cos 6, y = 3 + 2 sin 8…

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Q: Consider the following. Find y'(x). y'(x) = y = X = X x² +9 Find the critical numbers of y(x).…

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Q: Find the total differential. 8x + y 3z - 2y dw = W = 8 3z-2y dx + 3z- - 4y - 16x (3z-2y)² Jdy + (7…

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Q: The answers for N[T(t)], t=2hr, and t=5hr are wrong.

A: Given:To find: (a) To compute .(b) To find the number of bacteria present when .Note: After seeing…

Q: Find fx fy and f, and evaluate each at the given point. f(x, y, z) = xy x+y+z (3, 1,-1) fx(x, y, z)…

A: The given function is

Q: For this interval notation, draw its graph and write its equality: (-∞0, 6]

A: The given interval is .The aim is to sketch the interval and write its equality.

Q: Solve the equation for x in terms of the other letters. (Enter your answers as a comma-separated…

A: Given data

Q: Use spherical coordinates. Evaluate JJJ y²z² dv, where E lies above the cone 4 = 1/3 and below the…

A: G

Q: Use Lagrange multipliers to find the minimum value of the function f(x, y) =x² + y² subject to the…

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Q: The vectors (8,-12, 16) and (8, 12, 5) are orthogonal. Select one: True O False

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Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: The given polar curve .The aim is to find the slope of the tangent line to the polar curve at the…

Q: C T 3 2 1 To find the blue shaded area above, we would calculate: b So f(x) dx Where: 1 2 3 4 f(x) =…

A: We have to use the graph to find the integral substitutes and area  under the graph

Q: Evaluate the limit: limħ– →0 0-2 01/1/20 0 - 12/1/2 2 an ( 7 +h)-tan (7) h

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Q: 3 f(x) = x³ – 3x² + 4

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Q: Consider the following. {-x³ +3, -x² + 4x, x≤0 x > 0 Find the critical numbers. (Hint: Check for…

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Q: Solve the given initial-value problem. y(x) = 2y" + 3y - 2y = 10x² - 4x 13, y(0) = 0, y'(0) = 0 -

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