Use Theorem 13.9 to find the directional derivative of the function at P in the direction of PQ. f(x, y) = e2Y sin(x), P(0, 0), Q(2, 1)

Q: Find the gradient of the function at the given point. w = x tan(y + z), (9, 5, -1) Vw(9, 5, -1) =

A: Explained below

Q: How do you take the integral of sqrt(1+(e^-x)^2)?

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Q: E. Determine which equations are exact and not exact. Afterwards, solve for the equations hat are…

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Q: x'sec'ydy – (1 – 2x²tany)dx = 0 %3D

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Q: Evaluate xe*dx. -3

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Q: 2. 30e-3*(1+ e-3x)5dx

A: We need to evaluate integral.

Q: Two ships leave a dock at the same time, one sails northeast at the rate of 9 miles per hour and the…

A: Let A and B denote the first and second ship

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

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Q: In Exercises 5–8, choose rectangular or polar coordinates to set up an iterated integral of an…

A: To set up the integral of an arbitrary function f(x,y) over the given region.

Q: (25-у? 5-х SŠ s *²+y²dzdxdy

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Q: Determine whether each point lies on the line. x = -2 + t, y = 4t, z = 5 + t (a) (0, 8, 7) O Yes No…

A: topic - lines and points

Q: Note: you will need to find both the gener e homogeneous problem, and a particular so mogeneous…

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Q: S 3xe*dx

A: Given problem :- ∫ 3xex/2 dx

Q: The number of bacteria in a culture is increasing according to the law of exponential growth. The…

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Q: ( cos³x dx sin*x 9.

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Q: a2f_ If f(x, y) = xe?y + 6xy, then is given by: dydx O 2xe?y + 6 None of these e2y + 6 2 xe?y + 6 2…

A: We have to find the derivative

Q: Which of the following is a value of tan 0 if V3cos 0 - sin 0 = v2? -V3 + 2 V2 + 3 O Option 1 O…

A: Given  3 cos θ - sin θ = 2 We have to find the value of tan θ.

Q: 4v-16v²dv

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Q: Find the general form of f if f'(x)= 9f(x). f(x) = ]

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Q: What is the relative minimum value of the function f(x, y) = x° - 3xy + y – 2? Note: If the answer…

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Q: 2. * S arctan x dx 1 In(x²) + C C 1. x arctan x C A x arctan x -In(x² + 1) + C -- B 1 D x arctan x…

A: Solve the given integration

Q: Direction: Solve the following equations using separation of variables. 5. y*y' + y' + x2 + 1 = 0

A: To solve the following differential equation by using separation of variables. y4y'+y'+x2+1=0

Q: 8 4 4 -7 (a) h(x) = 7X 1 -7 (b) g(x) = 7x (c) k(x) = - 7X %3D %3!

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Q: z = 2 24 z=Vx² + y² 2 FIGURE 9

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Q: Direction: Eliminate the following arbitrary constants to obtain the DE. 5. x = c1coswt + c2 sinwt

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Q: In trigonometric substitution where the integral involves va? + u², what must be the value of the…

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Q: The sum of two numbers is 8. The product of the first number and the square of the second number is…

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Q: What is the lateral area of a cylinder with a height of 7 cmand diameter of 240 mm? 3360π cm2 1680п…

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Q: Determine whether u and v are orthogonal, parallel, or neither. u = -9i + 80j - k v = 9i + j - k O…

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Q: What is tan 0 if sin 0 = cos 0? -1 1 O Option 1 O Option 2 4 O Option 3 O Option 4

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Q: onsider the following planes. -4x + y + z = 4 12x – 3y + 4z = 16 a) Find the angle between the two…

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Q: What are the values of 8 between 0 and 2n (inclusive of 0 and 2t) that satisfy the trigonometric…

A: tan2θ-3secθ=-3⇒tan2θ-3secθ+3=0⇒2+sec2θ-3secθ=0⇒secθ=2, secθ=1⇒θ=π3+2πn, θ=5π3+2πn, θ=2πn

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: Consider the function y = 3(square root of x) + 8. What is the value of C in the interval [4, 9]…

A: First we will find fave

Q: At a point 160/3 feet from a building, and in a horizontal line with its base, the angle of…

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Q: d. x cosy + y sin x –1 = 0 3 х е. = 2 x y

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Q: Find the centroid of the solid generated by revolving the region about the indicated axis the area…

A: There is more than 1 question, as per the Q&A guidelines, We are answering the 1st question. If…

Q: 6.(Somewhat tricky) Use an appropriate substitution to solve: (a) dy y + x dx (b) (y³ + y?x) dx – x³…

A: To solve the following differential equation

Q: Sx² et* dx 1 e x (8x2 - 4x + 1) + C 16 (8x2 + 4x- 1) + C e4x 16 e4x 32 (8x2-4x + 1) + C e* (8x2 + 4x…

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Q: Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. y =…

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Q: s e8*(x³ + x²)sec² (x*e3* + 1) dx

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Q: An ice cream cone is filled with ice cream and surmounted ice cream in the formof a hemisphere on…

A: Given problem:- An ice cream cone is filled with ice cream and surmounted ice cream in the form of a…

Q: Evaluate using Linear Equations. v(dx/dv)=6ve²"+x(2v-1)

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Q: The barrel of a fountain-pen cylindrical in shape is 7 cm long and 5 mm in diameter. A full barrel…

A: Given that the fountain pen barrel is cylindrical in shape.

Q: 2t2 + 38 sinh 16t

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

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Q: Q3.3

A: We have to find the value of the given definite integral according to the given information

Q: Learning Task 4: Given the equation x2 +y² =9. 1. Differentiate using implicit differentiation. 2.…

A: Since, the student has mentioned to solve only part numbers (4) and (5), so we are solving part…

Q: uantity of cookies sold when the price per cookie, in cents, is x. Use this information to answer…

A: Since we are given with the multiple number subpart answered according to the guidelines

Q: dx x* +3

A: