Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y², (6,8, In 10)

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A: The given indefinite integral is: I=∫16θ2-9θ4dθ Taking θ2 as a common in the numerator,…

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Q: 2- Use the inversion method to solve the following system: x+3y+3z=1 x+4y+3z=0 x+3y+4z=-1

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Q: 2. Vy+1-2 dy

A: ∫vn dv = vn+1n+1+C

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Q: indefinite integrals: Show complete and detailed solutions. Express your answers in simplest form…

A: Using integration of square root of a2 - x2

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Q: dy – (x - y + 1)?dx = 0

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Q: Find the composite functions (f • g) and (g ). What is the domain of each composite function? (Enter…

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Q: Calculate the fluid force F on the shaded side of the triangular plate submerged in fluid with mass…

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Q: tan(2e) lim 30 Costue)

A: Solution is given below:

Q: Q2. Evaluate the integrals below by first using trigonometric identities to simplify the in-…

A: First simplify the integrand then integrate and simplify.

Q: b/ Find the solution to the homogeneous differential equation below dy x²+y² dx 2xy

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Q: For the following function f(x), determine whether there is an asymptote at x = a. Justify your…

A: For vertical asymptote ,set the denominator equal to zero .

Q: What is the a value of x such that sinx = .? 3 = 24.5° = 53.6° = 41.8° = 38.7°

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Q: Use the elimination method to find all solutions of the system of equations. (Order your answers…

A: By using elimination method to find all solutions of the system of equations.2x2-y2=17x2+5y2=14

Q: x4

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Q: 4. Consider the function f(x,y) = 4 + x³ + y² – 3x – 4y a. Find the values of x and y that…

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Q: x 1 + 1 -sisl y = 6. 2x Determine the arc length of the curve for

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Q: 1. Find derivative, critical numbers and the absolute maximum and absolute minimum values of f(z) =…

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Q: 10 (vi) / 1+ x dx x2 + 100

A: The given integral,     ∫0101+xx2+100dx

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 2y2 + 10, (2, 3) Vf(2, 3) =

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Q: 29. Which of following is the equation of the tangent line to the curve y = 2x - x² at the point (…

A: I am attaching image so that you understand each and every step.

Q: The graph shown below is f(x) = 2 cos x. If g(x) = Sřf(t)dt , find g '( 1 ). %3D 4 3- 2- 54 3 2 -1 1…

A: Use the Newton Leibniz Theorem and calculate the derivative.

Q: ) If we apply Rolle's Theorem to the function f(x)=2x^2−8x−4 on the interval [0,4], how many values…

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Q: Question Select your answer. A function f(x) has a critical number a = c. Which of the following…

A: Recall:  y = f(x) + C C > 0 moves f(x) up C < 0 moves f(x) down   Given P(x)=f(x)±k  Where k…

Q: Consider the expression (3x² + 2/x)10 a) Find a simplified formula for the general term. (separate…

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Q: Find the area bounded by y? = x3, y=2x

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Q: Solve the given differential equation by separation of variables. csc(y) dx + sec sec2(x) dy = 0

A: Solve the given differential equation by separable method.

Q: Your explanation should answer WHY you are doing the work and HOW you are doing the work briefly…

A: If f'x is:→ then fx is-ve→decreasing0→horizontal +ve→increasing=a & ≠0 →slant with slope…

Q: 1- use Gauss Elimination to solve the following set of equations: 3x-y+z=-2 x+5y+2z=6 2x+3y+z=0

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Q: 5. * 1 dx х (In x)3 1 + C 2 (In x)² 1 + C 3 (In x)2 A C 1 + C 2 (In x)? B D z+C 3 (In x) O A В E…

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Q: Evaluate the integral: J1 +2)³ 11 dx 44 1 22 1 89 O None of these 1 40

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Q: 4 -12 -10 -8 -6 F4 -2-1 6 10 12 -3 -5 LETTER BANK: Select the correct response(s).: 1: (2, 4] N:…

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Q: d) 2x³y + e2y = 4x + 5x²< e) y = (2x* + 4)4*

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Q: 2. Let g (x, y) = 2a² – y² . Compute g (1, 2), g (2, 1), g (1, 1), g(–1, 1), and g (2, – 1). - £(1…

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Q: the length of a child's square-based jewellery box is 5 cm more than its height. the box has the…

A: Topic  = Algebra

Q: find the Inverse LaPlace Transform, L-1{F(s)}. L~1 s2 А. (t - 1)*и(t — 1) В. t u(t - 1) C(t – 2)U(t…

A: Given, L-1{e-s/s²} We know that, L-1(e-s)= theta(t-1) L-1(1/s²)= t

Q: 4. V21-4x-x² dx

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Q: Can the Fundamental Theorem of Calculus be used to find

A: We have to check the validity of fundamental theorem

Q: S16 -X2 メー dy dx + x?+yz

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Q: Determine an equation of the form Ax t t Cz + D=O By for the plane that contains the line (x,y,2)=…

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Q: 2. Use the fundamental theorem of calculus part 2 to compute the integral 1° dr. 0,

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Q: The angle of shevation isdegrees loundtoenart )

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Q: Wt-1+2 dt

A: We will find the integral as following.

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

A: Solution According to Intermediate Value Theorem, a function f(x) is continuous and k is any number…

Q: Simplify arctan + arctan . O 0° 45° 90°

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Q: If f(x) and g(x) = In x, then (g o f)(x) =

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Q: Can the Fundamental Theorem of Calculus be used to find 5xcosx?dx?

A: This question can be solved by applying the second part of fundamental theorem of calculus.