3. Find S. F · dr where F(x,y, z) = (3y²e*, 6ye* F(t) = (sin t, ,2-) for 0

Q: 4. Find an equation of the tangent plane to the surface xyz = sin(x + y + z) at (1, −1,0).

A:

Q: Find a point on the surface x+4y--z² =1 where the tangent plane is parallel to the plane x+4y- z =…

A: we need to find gradient of given surface to know about direction of normal vector to tangent plane

Q: Find the equation for the tangent plane to the surface z=ln(4x2 +3y2 +1) at the point (0,0,0)

A:

Q: 6. Where does the tangent line to r = at the point (1, 0, 1) intersect the y-z plane.

A: Given:

Q: 63; Evaluate the întegral +3 dx + 6xy dy where Cay Curve Joininy (t, -) to (16, I),

A:

Q: 6. Set up but do NOT evaluate Evaluate the line integral 2 curve (t) - (t", t), where 0sts0. L ds,…

A: Consider the given integral as ∫Cyxds, where C is the curve r⇀t=t4,t3 and 0≤t≤1. Note that, the line…

Q: Find the slope of the tangent line to the curve of intersection of the graph of z = 2x2 + 3xy + 2y2…

A: We need to find slope of the tangent line.

Q: rea under the curve y = 2x – x² from x = 1 to x = 2 with n = 4 %3D tonglon

A:

Q: 6. Find the equation of the tangent plane to the surface: ==√√4-x²-2y², at (1,-1, 1)

A:

Q: Find an equation for the tangent plane to the surface z + 1 = xy² cos(z) at the point (1, 1, 0)

A: The given equation is z+1=xy2cosz. The objective is to find an equation for the tangent plane to the…

Q: 4. Find the equation of the tangent plane to the surface Z = = 5tan(x) – sin(3y) at the point (xoyo)…

A:

Q: Find an equation for the tangent line to the curve given parametrically by x(t) 2t, y(t) 4t2 +t+ 3 =…

A: we want to find the tangent lines to theparametric equations given byx=f(t)  y=g(t)The equation of…

Q: 1. Give an equation of the tangent plane to the surface z= In(4y – x) at the point (3,1,0).

A:

Q: The parametric equations of a curve are given by x = In (VE +1) and y = cosh-' (2t). dy when t = 1.…

A: Given x=lnt+1 and y=cosh−12t We have to find the dydx when t=1 We know that dydx=dydtdxdt.....1…

Q: Find equations for the tangent plane and the normal line at point Po (X0,Yo,Zo)(1,5,0) on the…

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: #5. Find an equation of the tangent plane to the surface with the equation 12x z = x²y*. y at the…

A: The given equation of the surface: z=x2y4-12xy Therefore: f(x, y)=x2y4-12xy Now:…

Q: 5. Find the length of the curve given by y= Vt* – 1 dt and 1<x<2.

A:

Q: How would you evaluate |F-dr, where C is the curve with param etrizati on r(t) for astsb?

A:

Q: Determine the equation of the normal line to the surface z2 cos(x + 2y) at the point (2, –1, 0).

A:

Q: The Normal line at the point (0, –1, 1) to the 3 surface exy - xy² + z³ = -2 is 7=y+1=² Select one:…

A:

Q: An equation for the tangent plane to the surface z + 3 = xy cos (2) at the point (3, 1, 0) is:

A:

Q: ompute the line integral ∫C [2x3y2 dx + x4y dy] where C is the path that travels first from (1, 0)…

A: The line integral is given ∫C2x3y2dx+x4y dy Consider fx,y=x4y22. ddxx4y22=12·4x3y2+22x4y…

Q: Find the are length of the curve 2x = 3 y over the interval from y=0 to y=1

A: To find: The arc length of the curve in the interval . Formula used: The arc length of the curve…

Q: Let C be the curve consisting of line segments from (0, 0) to (1, 1) to (0, 1) and back to (0, 0).…

A:

Q: Find the symmetric equations for the normal line LN to the surface S:f (x,y) = 5VT +y? at the point…

A: Given function is S:fx,y=5x2+y2. We have to find the symmetric equation for the normal line LN to…

Q: 4. Find the equation of the tangent plane to the surface ew + In(xz) - evz = 0 at the point (1,0,…

A:

Q: Use Green's Theorem to evaluate dr, where F-(VE+ 4y, 2+ C consists of the arc of the curve y 1z - z…

A:

Q: Evaluate S. (2xy – x²)dx + (x + y²) dy such that c is a curve bounded by y? – x , y – x² ?

A:

Q: Let C be the curve on the xy-plane that is the projection of a horizontal cross-section of the…

A: Given surface is,yz=ln(x+z) zxy=1x+z(1+zx)y-1x+zzx=1x+zzx=1y(x+z)-1 Take the derivative with respect…

Q: Find equations for the a) tangent line and b) normal plane to the curve 1 x=t- cost, y = 3+ sin 2t,…

A: x=t-cost, y=3+sin2t, z=1+cos3t We know that rt=xt, yt, zt dxdt=1+sint, dydt=2cos2t, dzdt=-3sin3t At…

Q: Find the tangent plane to the equation z 2y cos(5x – 4y) at the point (4,5, 10)

A: Given; z=2ycos(5x-4y) at the point (4,5,10)

Q: 13. Find the point on the curve 7(t) = (2 sin t, 2 cos t, t), 0<ts 7, where the tangent line is…

A:

Q: 4. Find the equation of the tangent plane to the surface ey + In(xz) – evz = 0 at the point (1,0,…

A: Given:

Q: 9. Find an equation for the tangent plane and the normal line to the surface xy + yz + zx = 5 at the…

A: f(x,y,z)=xy+yz+zx-5=0,  at  (1,2,1)now we differentiate above equation with respect to x,y,z…

Q: Compute 2z dz (2² – i)3 when y is any arc z = z(t) in C with |z(t)| > 2 for every t, with…

A: Let the required arc be ABC, which starts at z=3 and ends at z=2i: The shaded area shows a sector…

Q: 3/Find the equation for the tangent plane and normal line to the surface Z=9-x² + y² at the point…

A:

Q: Calculate the curve integral ∫c ( 3x2 - 3yz + 2xz )dx + ( 3y2 - 3xz +z2 )dy + ( 3z2 - 3xy + x2 +2yz…

A: Using green's theorem to find the line integral.

Q: Find the exact length of the curve defined by x = 3 cos t – cos 3t and y = 3 sin t – sin 3t on the…

A:

Q: Show that the surfaces S1 : 4x + y° + 9z² = 108 and S2 : xyz = 36 are tangent at the point (3, 6,…

A:

Q: Graph the curve. x = cos(t) + In(tan(t/2)), y = sin(t), A/4 sts 3/4 y y 1.2- -0.3 -0.2 -0.1 0.1 0.2…

A: Using graphing calculator we graph the function Answer(a):

Q: . Find SF dř where F(x,y,z) = (3y?e*, 6ye* -, 1+) and C is the curve F(t) = (sin t, ,2-) for 0 stsn.

A:

Q: Let C be the curve which uses straight line segments to travel from (0, 0) to (0,1) to (2,0) and…

A: The curve C is the line segments travels from 0, 0 to 0, 1 to 2, 0 and then back to 0, 0. Draw the…

Q: 1)Determine the equation of the tangent line to the intersection of the surfaces x²-y=0 and y+z²=16…

A:

Q: Compute the equation of the tangent plane to the surface: y = 1 - x2 - 2z2 At the point (0, 1, 0)

A:

Q: Determine the equation of the normal line to the surface z2 = cos(x + 2y) at the point (2, –1,0).

A: We have  z2 = cos(x+2y) ⇒cos(x+2y) - z2 = 0  So, F(x,y,z) = cos(x+2y) - z2  Thus,  ∇F(x,y,z) =…

Q: Let F(r, y, z) = (y² + 2z, 2ry + 4, 2a), and let the curve C be described by x = t, y = t, z = t3…

A:

Q: what is the length of the curve y=1-cos(x) from x=0 to x=4pi

A: The given curve is  y = 1 - cosx dydx=0 - (-sinx)  =sinx

Q: 3. Find the equation of the tangent plane to the surface in R³ defined by z = 2x² + y² at the point…

A:

Q: Use Green's theorem to evaluate S. (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

A: According to the given information, it is required to use green’s theorem to evaluate the integral.