Find an equation of the tangent plane to the given surface z = x sin(x + y) at the point (-1, 1, 0).

Q: Question 9 A mine cable weighing 60 N/m is unwound from a cylindrical drum. If the lower end of the…

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Q: Evaluate the integral below by interpreting y=f(x) it in terms of areas in the figure. A1 The areas…

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Q: Calculate s f(x, y, z) dS for the given surface and function. D(r, 0) = (r cos(0), r sin(0), 0), 0<r…

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Q: A farmer finds that if she plants 40 trees per acre, each tree will yield 20 bushels of fruit. She…

A: Harvest

Q: Given r = (5, 2, 3) and s = (-4, -2, 2) and t = (3, 4, 1) %3D a. Write the unit vector for S b.…

A: This question can be solved using the concept of unit vector and linear combination of vectors.

Q: Find the general solution for the differential equation. y' = 2 - x³ + x6

A: Given query is to find the solution of the differential equation.

Q: Evaluate the integral using the following values. 8 8. x3 dx = 960, x dx = 24, dx = 4 x3 dx

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Q: dr

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Q: Find the polar equution for the cartesian curve r=8 sin o Cos o r=8 sec e tan E r=8 sine tan E r=8…

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Q: Differentiate. 9. y = e

A: As per the guidelines I am sharing the solution to the first question.

Q: Verify the Divergence Theorem by evaluating F.N dS as a surface integral and as a triple integral.…

A: Here, using the Divergence Theorem, ∯F·Nds=∫∫∫v∇·Fdv Here, F=xy,z,x+y So, ∇·F=∂F∂x,∂F∂y,∂F∂z=y,0,0

Q: Question 16 Find the equation of the tangent plane to the given surface at the indicated point. x2…

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Q: 5 and 6 8 and the angle between a and b is 0 = 75°. Given a a. Construct a well labelled diagram for…

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Q: am confused can you highlight answers please thank u

A: From the original solution the answers are: Intercept: 0, 0 Relative minimum: -5, -110 Relative…

Q: 4x d.x J V3 - 4x – 4x2

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Q: -3 2. (2x+4)3 8x dX use integration by parts and then find the value of definite integral.

A: A detailed solution is given below.

Q: 4. If the larger of two numbers is subtracted from six times the smaller, the result is 20. If twice…

A: The detailed solution is given below Thank you

Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Show…

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Q: 2 Find the cartesiun equation for the polar Carre rこlcos . Al(x-2)²+y2=4 ty²-4 %3D c)x²+ Cy-2)?=4 D)…

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Q: Express the integral as an equivalent integral in which the z-integration is performed first, the…

A: Here,  0≤x≤4-yy≤z≤8-y0≤y≤4 To change the order of integration to dx dz dy to dz dy dx

Q: Use double integration to find the area of the plane region enclosed by the given curves. y = 81 – x…

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Q: Perform the following integration. If a u-substitution is needed, indicate the choice for u. So xe…

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Q: Find the area bounded by the graphs of the indicated equations over the given interval.     y=−ex​;…

A: Note:- Here your equation of equation we use y=-ex , y=0 , -2≤x≤1  Given problem:- Find the area…

Q: Inx F (x) = So It dt %3D

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Q: Simply the integral dx using am X²+4 A a ate trigonometric substitution. S sin edo DS sec edo dS1de…

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Q: dr a 2 1 +3

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Q: If g(x) is differentiable at the point x and f(x) is differentiable at the point g(x), then f{g(x)}…

A: If g(x) is differentiable at the point x and f(x) is differentiable at the point g(x), then f{g(x)}…

Q: Evaluate the definite integral. (Round your answer to two decimal places.) 1 9 (cosh(x))² dx

A: cos h(2x)=cos h2x +sin h2xcos h(2x)=2cos h2x -1cos h(2x)=1+2sin h2xcos h2x =1+ cos h (2x)2

Q: 9. 5+ 8 7- 6- 3 5 4 2 g(x) 2 h(x) 1 1 1 2 3 x-values 4 5 1 2 3 x-values 4 If f(x) = g(h(x)), then…

A: Explanation of the answer is as follows

Q: Evaluate the integral 7x sin y dy dx. 00 The value is (Type an exact answer, using x as needed.)

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Q: 4- if U(x,y) = x2 + 2y and x(r, t) = r sint, y(r,t) = sin?t, au find 1- ar au and 2- at au 1- ar ди…

A: Given that,   U(x,y) = x2+2y   and x(r,t) = rsint,     y(r,t) =sin2t we have to find ∂u∂r,    ∂u∂t…

Q: A population of yeast cells can double in 6 hours. Assume an initial population of 4,000 cells. What…

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Q: 3 Evaluate the integral c Ħ A) 1 B) 77 c) - Ť tan?xdx E)ユ-

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Q: Q3) Apply the logarithmic differentiation to find the derivatives of: x+1 y=(sinx-x)**

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Q: Question 5 3 Consider the function f(x) = Let F(x) be the antiderivative of f(x) with F(1) = 0. Then…

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Q: How much work is required to pump all the water from a right circular cylindrical tank, that is 8…

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Q: Ise Part 1 of the Fundamental Theorem of Calculus to find the derivative of the fum 8(x) = [" 1 dt t…

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Q: Use double integration to find the volume of the solid bounded by the cylinder x² + y? = 16 and the…

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Q: Solve the differential equation. dr sin 0- do +(cos 0)r = tan 0, 0<0<,

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Q: Find the work done by F in moving a particle once counterclockwise around the given curve. F= (x-…

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Q: 5. Write an expression equal to - log. (c) · log (b) |using exactly one log. (hint: the base of the…

A: To answer the given question of logarithms.

Q: Determine the directional derivative of f at the specified point and direction. f(x) = x³ + y³ – 3x2…

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Q: ​(A) Find the average value of the function over the indicated interval.   ​(B) Graph the function…

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Q: dy_ y -1 dx

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Q: Optimize Z= In(4x2 - 24x + 2y2 - 20y) optimize the function. Find Zx, Zy, Zxx, Zyy, Zxy. Comment…

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Q: / (3Vi-1)dt is 3 -1 by the 2nd fundamental theorem of Calculus. The derivative with respect to x of…

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Q: dy x(2lnx+1) dx sin y + y cos y

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Q: -dx is an improper integral. A) True B) False

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Q: 1.

A: Given,  ∫1+∞1xdx

Q: .W (3) Solve the following differential equations of

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