6. Determine an equation of oNE of the two lines tangent to the curve x?y +2xy² = x + 6y, when x = 2.

Q: 3. Let f(r, y) =rsin ry. Find: %3D (a) fz(I, y) (b) fy(r, y) (c) fyy(1, 9) (d) fyz(r, y)

A: Given f(x,y)=xsin(xy) Now fx= d/dx (f(x,y)) fy= d/dy (f(x,y)) fxx= d/dx(fx(x,y)) fyy= d/dy (fy(x,y))…

Q: Find the volume of a cone with a base radius of 3 in and height of 10 in. Do not round. Be sure to…

A: Find your answer below

Q: 3. Determine the differential coefficient of y + 2x - 3 when x = 7 %3D

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Question 8 of 10 v(x) = 4 cos(sin(3x)) Select the correct response: –12 sin(3x) cos²(3x) -12 cos(3x)…

A:

Q: Find the limit. NOTE: Enter the answer using round brackets. t² + 8 1' lim t→+∞\ 9t² + 10't (?, ?)

A: We can solve this as follows:

Q: N= N, - 0.2 t ,e

A: To find dN/dt for the followingN=N0e-0.2t

Q: Ans: -+ cosx c 1. y' +y2 sin x = 0

A:

Q: NG) Find T(t) and N(t) at the given point. T r(t) = 8 cos(t)i + 8 sin(t)j+ tk; t = T()= NE) -| ||

A:

Q: Solve the boundary value problem y" – 10y' + 25 y = 0, y(0) = 3, y(2) = -2. %3D %3D

A:

Q: da. Evaluate the integral Ja2 + 25 1 (a) -( :+ 25)을 + 25(교2 + 25)을 + C (x2 (e) * + 25) + * + 25) +C…

A:

Q: Use cylindrical shells to find the volume of the solid generated when the shaded region is 1…

A: Let's find.

Q: Find the total area of the region enclosed by y=x^2 and y=2x by integrating with respect to y. (A)…

A: To find the area of the region enclosed by the two curves.

Q: Two linearly independent solutions of the differential equation y" + 6y' + 9y = 0 are Select one: yi…

A: characteristic polynomial  r2 + 6r + 9 =0 (r+3)2 =0 r = -3 solution of this eqaution is y(x) =…

Q: Evaluate the definite integral. e6t i + e¬j +t k )dt O e6 - i - e- 6. + (e* – 1) i – (e-1 – 1) j + k…

A:

Q: u(x) = (tan? x – a²)³ - Select the correct response. 3(2 sec? x tan a- 2x)(tan? r- a²)² o 3(tan? r –…

A: Given that       u(x) = (tan2x - x2)3

Q: Given that y = 3e is a solution of the differential equation %3D y" + 3y' = 0. Then, by using…

A: Follow next step

Q: 2x4 h(x). 5x3 + 6 Select the correct response:

A:

Q: Find equations for the tangent plane and the normal line at point Po (Xo.Yo.Zo) (1,2,0) on the…

A: Let,  ϕ=-8cosπx+3x2y+exz+5yz-15∇ϕ=i∂ϕ∂x+j∂ϕ∂y+k∂ϕ∂z…

Q: 1- (2 xy-4 y) dx+(3x²y-8x) dy30

A:

Q: 3) Water is being poured at the rate of 2TT m3/min. into an inverted conical tank that is 12-meter…

A:

Q: 1 (x-1)(2x3+2x2+3x+2) x3 (x+1) dx

A:

Q: 2.x h(x) = 5x3 + 6 Select the correct response: 8.x3 15x2 +6 10x + 48x (5r + 6)2 10. + 6x® 5x3 + 6…

A:

Q: Find and sketch the domain for the function. f(x.y) = In (x? + y? - 4)

A: We can solve this as follows:

Q: 3. Determine the differential coefficient of y =-+2x – 3 when x = 7 4. If f(t) = 3 sin(4t + 0.12) –…

A:

Q: Find the arc length of the parametric curve. x = 4 cos(t), y = 4 sin(t), z = 3t; 0<t< T L =

A: Given parametric curvex=4 cost , y= 4 sint  , z=3t ;  0≤t≤π

Q: For time, t, in hours, Osts1, a bug is crawling at a velocity, v, in meters/hour given by 7 v = 6 +t…

A:

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

A:

Q: (x³-4) dx x3+2x2+2x

A: Here we have to integrate the given Integral.

Q: d/dx integral from e to x^3 ln(t^2+1)?

A: If Fx=∫b(x)axf(t)dtthen dFxdx=ddx∫b(x)axf(t)dt=faxa'x-fbxb'x

Q: Find the gradient of the function at the given point. w = x tan(y + z), (14, 11, -6) Vw(14, 11, -6)…

A:

Q: 1. Find the maximum value of r+y subject to the constraint r + y? = 18.

A: The maximum value of x+y subject to the constraint x2+y2=18

Q: 3. LetR be the region shown in the accompanying figure. Fill in the missing limits of integration.…

A: Given problem:-

Q: dx Evaluate the improper integral x(In x)?

A:

Q: Question 5 of 10 r(x) = cot2(3x² + 1) Select the correct response -6x2 csc(3r? + 1) cot (322 + 1)…

A: r(x)=cot23x2+1Differentiate w.r.t.xr'(x)=ddxcot23x2+1Apply chain…

Q: Find the area of the surface generated by revolving the given curve about the y-axis. I = 8y + 3,…

A: Given that the curve x=8y+3, 0&lt;=y&lt;=3  To find the Area of Surface generated by revolving the…

Q: d. dt d Calculate ri(t) - r2(t)] and ri(t) x r2(t)] first by differentiating dt the product directly…

A:

Q: 5x 8. 10e dx

A:

Q: Find the area of the shaded region. The y=- Consider c=64. Enter the exact answer. ver. Area

A: To solve the following problem

Q: 2.x4 h(x) = 5x³ + 6 .

A:

Q: f(x + Ax)-f(x) D. APPROXIMATE DERIVATIVES f(x) = Ax 8.) 2A

A: Given function f(x)=2x

Q: If a > b, it is possible to have log,(a) < log.b). (As usual with logarithms, a and b are positive…

A:

Q: dx 1-S, 4+x2

A:

Q: Work Problem 1( Use implicit differentiation to find dy/dx where x+7y10 = 3

A:

Q: 5- S(tanx + secx)² dx

A:

Q: 2) Zy? + X :0 + x -1 :0

A:

Q: Solve the following Initial Value Problem using Laplace transform: y" – 9y' + 8y = e-8t ; y(0) = 1,…

A: The given equation is  y''-9y'+8y=e-8t; y(0)=1,y'(0)=1

Q: Answer all questions in the space provided. Show ALL your steps in your calculations. Answer in…

A: According to bartleby guidelines I can only answer the first three subquestions. Please repost the…

Q: A spring whose natural length is 13cm exerts a force of 37N when stretched to a length of 18cm. (a)…

A: Given that the spring whose natural length is 13cm exerts a force of 37 N when stretched to a length…

Q: 4) A particle is moving along the curve y = vx. As the particle passes through the point (4,2), its…

A:

Q: If a building contractor hires 8 day laborers and 2 concrete finishers, his payroll for the day is…

A: