6. Given f(x,y) = x² – 2xy² – 4xy + 5. Find all the critical points of f and determine the nature of each of the critical point. - UTM UTM UTM

Q: Solve the exponential equation algebraically. Approximate the result to three decimal places. (Enter…

A: To solve the given equation algebraically

Q: S etanx sec²x dx

A:

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A: We need to find How many servings of each food should be given to the patient.

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Q: The length of the curve determined by equations x = 8 cos t + 8t sin t and y = 8 sin t – 8t cos t…

A: arc length

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A:

Q: 4. x(x² – 1)² dx

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

Q: Find the volumes oF the solids geverated by revolving +he regions bounded by the graphs oF the…

A: Given:-  the region bounded by  y=2x2y=0  and x=2rotating about the x-axisusing washer/disk method…

Q: Describe the graph of the equation. r = 14 sin 17t i – 14 cos 17t j O It is a circle of radius 14 in…

A:

Q: for the N(0) is it 0k? or can I write it just k?

A: Yes, N0=-12i+12j+0k.

Q: Solve the following problems. 2. 2x°cos 5y+ x tan5y dy=0

A:

Q: Find the tangent plane to the equation z 5z° + 4y – y at the point (4, 2, – 66)

A: Given: z=-5x2+4y2-y      4,2,-66

Q: (3t – 1)66 dt

A:

Q: Describe the graph of the equation. = 6 cos t i + 2 sin t j -k O Itis an ellipse in the z = -1…

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Q: Use the chain rule to find and , where as z = x² + xy + y, x = 6s + 9t, y = 5s + 8t %D First the…

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Q: xー1 dx (x+1) (x-3)5

A: Use substitution method for solving the  integral.

Q: 2. y = e*cos (2x) is a solution to y'-bytoy=0 3X

A: 2.y=e3xcos2x is a solution to y''-6y'+13y=0

Q: 5. What is the general solution of the following differential equation ( .6³yod?y =0)? ,d*y +9. dx2…

A:

Q: Determine if the following function is continuous or discontinuous at x = 0? 4z +5 f(2) = %3D 9- 32

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Q: At a seaport, the depth of the water during the day can be found using the equation h = 6.0 cos (…

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Q: Evaluate the following algebraically. csc? x lim 1 O 1 O -1 8. 8.

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Q: Integration

A: We will solve the integral.

Q: roduct directly and then by applying the formulas dr dr r(t) and dt dr, dr x ). dt Fi(t) - cos(t)i +…

A: To differentiate.

Q: Perform the addition or subtraction and use the fundamental identities to simplify. There is more…

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Q: 8 Evelluate the double integral: + 3x) dydx

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Q: 2 ー (4-x²) dx -2

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Q: Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall…

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Q: Find f, and fy! and evaluate each at the given point. xy f(x, y) = (7, –7) X - y fy(x, y) %D f,(7,…

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Q: Show that the function f defined by 1, (x, y) = (1, – 1) f (x, y) : .2 x + y (x, y) # (1, – 1) x + y…

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Q: Apply different integration techniques in solving the integrals. - Properly carry out integration…

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Q: If the tan x 1.5 then what are equivalent expressions to cot x ? Select all that apply. 1 1.5 3 1…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: Vector

Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

A:

Q: 1. 2x2 + 4x + y = 0,y = 2x %D %3D

A: Given :

Q: 1. The approximate value of -31.8 using linear approximation O -2.0025 O None of the choices O…

A: Ni

Q: For the curve y = f(x) = x², 0 < x < 2, its length is 2 dy` dx - {(aV17+ In (4 + v17). VI7). L 1+…

A: Apologies for the inconvenience. The correct solution is given below: Given that y=x2 Hence, dydx=2x

Q: Given z = f(а, у), а — г(и, v), у — у(и, v), with 2(0, 2) = 1 and y(0,2) 4, calculate z,u(0, 2) in…

A: We have to find the value of zu(0,2).

Q: 5. Lva – 2r dx 6. 5x+2

A:

Q: Find the series radius and interval of convergence for what values of x does the series converge x"…

A: We need to find radius and interval of convergence.

Q: 3 Consider the function g(x)= sin --1| with restricted domain [0,4]. Find and identify any relative…

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Q: Evaluate the definite integral. 1+eJ+/k]di i-ej+ k o ? - 1 1 + (-" – 1) j + k e-1)1- (e - 1) J+ k o…

A: Given: I=∫01e9ti+e-tj+tkdt As we know that; The Power rule: ∫xndx=xn+1n+1+C And ∫eax+bdx=1aeax+b+C

Q: 5. What is the general solution of the following differential ,d*y 6. equation 'dx+ d³y.od?y dx2 dx3

A:

Q: W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable. %3D If u(1, — 3) — 7, и, (1, —…

A:

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: 6. Find equations of the tangent line and the normal line to the curve y = 1+ x2 at the point (1,)…

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Q: Use Disk Method only Find the volumes of the solids generated by revolving the regions bounded by…

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Q: S 2y(yª – 4)¯³ dy

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Q: Find r'(t). r(t) = (tan¬(11t))i+t cos(t)j – vtk NOTE: Enter your answer in terms of i, j, and k.…

A: Here, the given vector function is: r(t)=(tan-1(11t))i+tcos(t)j-tk

Q: The following series is divergent: (8")(10") (7")(9")+1' n=1 Select one: O True O False

A: