A curve is given implicitly by the following equation .2 (x + y)² + x²y = 11 Find the slope of the tangent line to this curve at the point (x,y) = (1,2).

Q: Let flx) = S.5 1 dt. o t4 +5 Find the derivative f'(x). none of the choices O e2x O ex

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Q: Example -3 .2 Evaluate I (x+ 2y – z) dx dy dz I (x + 2y – z) dx dy dz - 2 SLE + 2xy – xz dy dz - 2…

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A: Given problem:- If a ball is given a push so that it has an initial velocity of 24 ft/sec down a…

Q: Work Problem 1 (With integrity statement] Let R be the region bounded by yx+ 2, y=0, und x=2. Draw…

A: To find the value of given double integral.

Q: dr Evaluate: EV9 + 4 A f (x) = = - 9r² + 4+2 +C 3x B f (x) = -4 ln 9x² + 4+ 2 +C 3x ©f(r) = -2 In…

A: A detailed solution is given below

Q: dx Evaluate: (x-4)(x-1) X-1 + C x- 4 A B None of the given choices 3ln + C x-4 - 4 + C x- 1 D X- 4 E…

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Q: S sin x (cos x)ådx (cos x)ž + C none of the choices (cos x)Z + (sin x)ž + C O A B.

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Q: Find the point of inflection for the function f(x) = 5x - 14x2- 11x+1 O (-2.2, 37.72) O (2.2,…

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Q: x2 In solving for the antiderivative of f(x) = Fusing trigonometric substitution, Jf(x)dx is V4- x²…

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Q: S sin?x cos³x dx i sin*x -sin*x + c i sin*x +sin°x + C O A B -sin'x -sin'x + d

A: The given integral is ∫sin3xcos3x dx We evaluate the integral using proper substitution. At first we…

Q: Write T if the statement is true, or F if it is false. W. 1. -dx x' +C 3 %3D 45x=-5x +C 9. 2. %3D 4…

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Q: Let R be the region bounded by y =x+4, y=0, and x=4. Draw the region R, and evaluate the following…

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

Q: 104. x + 4xy – y³ = 6

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Q: Je* cos (7e*) cos (4e*)dx Evaluate: @ --co (3e*) -cos (11e') + C (3e*) – -cos (11e*) +c A 6. 22 ®…

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Q: Sy+1-2dy can dy = 4x(x²+2)dx. be evaluated conveniently if we let x VVy+1-2 and True False

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Q: Use the Midpoint Rule for the triple integral to estimate the value of the intergral. Divide B into…

A: Note that, 0≤x≤4, 0≤y≤8 & 0≤z≤4 generate the cube. And, the mid-points of the cube are:…

Q: dy = 2/y- 5In|Vy+5| + C Vy+5 (A) True B) False

A: we will use basic integral rules and the method of integration by substitution.

Q: S sin³x vcos x dx 2 Vcos7x + Vcos³x + C |cos³x 2 Vcos³x + C B 2 Vcos"x -Vcos?x + C Vcos³x + C none…

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Q: dx Evaluate: xV x2 +4 (A None of the given choices ® n Vx2+4- 2 + C x² + 4 +2 Vx²+4-4 +C x² + 4 + 4…

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Q: Apply the chain rule to differentiate the following functions. Show your complete solutions and…

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first question. If…

Q: Differentiate the function:  k(x) = 4 ln (x) + 2 cos x + x^2 k'(x) =

A: k(x)=4ln(x)+2cosx+x2Differentiate with respect to xk'(x)=(4×1x)+2-sinx+2xk'(x)=4x-2sinx+2x

Q: Determine if the equation is separable. If so, solve the initial value problem. " e'y'(t) = t (In…

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Q: Solve the following Initial Value Problem: y"+ 16y 0, x)= 2 and y'() = 5. %3D

A: Topic = Differential equation

Q: 4.) f (x) = %3D x3 5.) f (x) = 2x² + Vx

A: we have to find the differentiation of given function

Q: UsinG PYTHAGORE AN IDENTITY, SOLVE FOR [sin Gx) - cos (Vx)] - 3x5 COS

A: The integration of the integral is  [sinx1/3-cosx1/3]2/(3x2/3).

Q: 1 In solving the antiderivative of f(x) = 3sin(x) + 4cos(x)+ 5 by miscellaneous substitution, the…

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Q: Determine an antiderivative, y, of the given derivative, y. Then use the given condition on y to…

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Q: sin x xý + 3y += x2

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Q: 3 dx (3) x? +9 -3

A: Topic = Integration As per guidelines , At a time only one question can be answered. please repost…

Q: 25 – x² In -dx , if we let u=/25- x2 , then udu= – xdx. T True F False

A: Follow next step

Q: I. Evaluate the triple integral zdV, where E is bounded by the cylinder y? + z? = 16 and the planes…

A: Let's find.

Q: cos 2x sin'x dx can be evaluated by factoring sin x as (sin?x) 2sinx and transform sin?x into 1-…

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Q: What is the derivative of f(x) =2cos (x)? %3D 2 cos (2x) O -2 cos (2x) O 2 sin (2x) -2 sin (2x)

A: f(x) =2cos2xdifferentiating w.r.t xd(f(x))dx=ddx(2cos2x)

Q: z+3 lies on the y -axis of complex plane, where Q48. If z = x + iy and z + 3, then which of the…

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Q: 2x + 1 -d.x J (3x – 1) (x² + 2.x + 2)' Evaluate:

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Q: O Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx 2, y =

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Q: Which of the following yields the value 318? 3 (8х + 7у) dxdy 0 °0 (8x + 7y) dydx 0 °0 none of the…

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Q: Find the slope of the tangent line of the function y = In (x) at x = e2 O1/e? 4/et O 1/e* O 2le2

A: Topic = Derivative As per guidelines, At a time only one question can be answered out of different…

Q: A chemical manufacturer sells sulfuric acid in bulk at a price of $100 per unit. If the daily total…

A: In this question we have to find how much is the daily maximum profit ( in dollars).

Q: olve the following Initial Value Problem: y" + y-6y 0, y(0) = 2 y (0) = -1. and %3D %3D %3D

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Q: prevents changes to this answer. Which series converge in the interval described by x<1? 1.…

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Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

A: Given that the tetrahedron enclosed by the coordinate planes and the plane 7x+y+z=4.

Q: Question 4 -e-*) dx Evaluate: A '+C 2 B cosh x +C sinh x +C D – sinh x +C E None (F -cosh x +C 2

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Q: II. Multiple Choice: Read and understand the statements, then choose the correct answer. - Write the…

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Q: If f(x) = 2x + Ax?+ + Bx – 5, find the value of A when f(2) = -3 and f(-2) = -37 -5 -3

A: A=-15/4

Q: Suppose that y, denotes a nontrivial solution of the following second-order differential equation:…

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Q: Find al ales of that satsy th equation f(x)= g'(x) # f(x)=sin x and g(x)=cos x. 3mt x+kT, where k is…

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Q: In x²/25+ x² dx , we let x=5sine. A True

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Q: | cos ?x sin'x dx can be evaluated by factoring sin'x as (sin²x) ²sinx and transf sin²x into 1-…

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Q: 2X + Y+ 6z= 9 8X + 3Y + 2Z= 13 X + 5Y + Z= 7 X=2 Y=4 Z=15 O X-1 Y=1 Z=1 O X=1 Y=2 Z=1 O X=4 Y=2 Z=-7…

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