p(x) = Describe the fibers of y.

Q: find a parametrization for the curve. the line segment with endpoints (-1, 3) and (3, -2)

A:

Q: d. The curve y= In x , y-axis, the lines y 0 and y 4.

A: Given, We have to find area of region bounded by  y = lnx ; y axis ; y =0 and y = 4.

Q: Show that the inflection points of the curve y=  x sinx  lieon the curve y2(x2 +4)  =4x2 .

A:

Q: Find the curve length 0 +2),0<ys4 0 < y

A: 76/3

Q: x = X, +(-

A: let the initial velocity be v0 , and the initial distance be x0 .and in time t , the new velocity…

Q: What is the linearization L (x) of a function ƒ(x) at a point x = a? What is required of ƒ at a for…

A: linearization is finding the linear approximation to a function at a given point.It is given by,

Q: sketch the graph xyz plane x^2+z^2=4

A: GIVEN: x2 + z2 = 4

Q: Tangent to the curve z2 = 2xy + x2 , z = 3 , at the point ( 1, 4, 3) %3|

A: For a surface of the form: f(x, y, z)=0, the equation of the tangent at x0, y0, z0 is defined as…

Q: 6. Use a property of derivatives of vector valued functions to show that # [F(t) × F'(t)] = F(t) ×…

A: to show ddtrt→×rt→'=rt→×rt→'' we will use  ddtu→×v→=u→ddtv→+v→ddtu→

Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: Find the moment of inertia of the area of the loop y2=x2(1-x), with respect to y-axis

A: We have to find the moment of inertia of the area of the loop y2=x2(1-x), with respect to y-axis.

Q: Tangent to the parabola z = x² + 3y² , x = 1 , at point ( 1, 2, 13

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: c. y = 2Vx when x = -1 с.

A: We have to find the gradient

Q: Q5] What is a parametric representation of a curve? What is its advantage?

A: We are entitled to solve only one question at a time so we will answer only the first question.…

Q: How will the contour maps of f (x, y) = x and g(x, y) = 2x with contour interval 1 look different?

A: To describe how the contour maps of f(x, y) = x and g(x, y) = 2x with contour interval 1 look…

Q: Find an equation for the tangent plane to z-x-y = 3 at the point (2, 1, 8) Z - ) %3D

A: given z-x2-y2=3 at point 2,1,8

Q: b. y = 2x2 when x = 6 %3D 3.

A: Consider the curve: yx=2x23 at x=6. Find the gradient of the curve at x=6.

Q: Where does the normal line to the parabola y= x- x2 at  the point (1, 0) intersect the parabola a…

A: Normal to a curve is a line which is perpendicular to the curve at its point of intersection with…

Q: Find curl F if F(x,y,z) = 16yºzº i - 8x³z8j - 7xy4 | curl F = (-28xy3 + 64x³z7) i+ (7y4 + 80y5zª)j+…

A:

Q: find a parametrization for the curve. the line segment with endpoints (-1, -3) and (4, 1)

A:

Q: The line that is normal to the curve x2 + xy - 2y? = 0 at (3,3) intersects the curve at what other…

A:

Q: Find the image of the line y =-x under the mapping = f(z) =2² + 4z %3D %3D

A: We need to find the image of the line y = - x under the given mapping.

Q: e point on the plane x+y+z:

A:

Q: Find the gradient of the function y = x³ + x² – 2x at points where - a. It crosses the x -axis b. It…

A:

Q: Describe the traces of the curve x2 + 9z2 = 9 in the vertical planes (those parallel to the…

A: The traces of a surface are the cross-sections created when the surface intersects a plane parallel…

Q: Find the distance from the x-axis to the plane z = 3.

A: Given equation of plane - z = 3z-3 = 0       ................(1)General equation of plane is given…

Q: Haw J Express the fallasing function by Cartesian equationst 3K34tane Seco

A:

Q: 3- Find the length of the curves in Exercises 1-4. X = (y3/2/3) - y¹/2 from y = 1 to y = 9

A:

Q: Find the distance between the pointx1 =−1, y1 =1, z1 =3 and the point x2 =1, y2 =1, z2 =1.

A: The first point is (-1,1,3) and the second point is (1,1,1) We will use the distance formula:

Q: Find the points on the cone z = x² + y² that are closest to the point (-5,-2,0)

A:

Q: Orthogonal Trajectory of the Curve x2+y2 = 2 In Cx

A: From the given curve; x2+y2=2lncx Now differentiate with respect to x. So,…

Q: Differentiate the function. y = In(In x) y' = %3D

A: Given y=ln(ln x)             y=ln(ln x).y'=ddx(ln (ln x))y'=1ln(x) . ddx(ln x)y'=1ln(x) . 1xy'=1x .…

Q: Findauihtvectorhermat to thesuFace X Y +X2=1 et the Point (-1,1,1)

A:

Q: Differentiate the function. y = (In x)4 %3D y' = %3D

A:

Q: Determine the gradient of the curve 3xy + y² = -2 at the point (1, -2)

A:

Q: Tangent to the curve z2 2xy + x² , z = 3 , at the point ( 1, 4 , 3 )

A: Consider the curve, z2=2xy+x2 ⇒x2+2xy-z2=0

Q: Region Ris enclosed by the curve y = 2 Vx – 3, the line y = 4, and the line a = 3. y = 2/z – 3 y = 4…

A:

Q: 1 y == (x² + 4)°%2 ,0 sxS 2 (x2 + 4)°/2 ,0<x< 2 6. deur die berekening van die volgende bej…

A: The given function y is - y = 16x2+432     ........(1)Formula for calcualting the lenght of a curve…

Q: integral that line x = 0

A: As per the bartleby guidelines for more than three parts only three has to be solved. Please upload…

Q: Find the linearization of f(x,y) at the indicated point (Xo.Yo). f(x,y) = In (x +y): (4, 5) L(x,y) =

A:

Q: What does parseval's identity imply about relationship between the dot products x · y and [x]ẞ·…

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: Tangent to the curve z2 = 2xy + x² , z = 3 , at the point ( 1, 4 , 3

A:

Q: (2) find the (x,y) coordinates of all points of intersection ot the curves.

A: b.(2) Given the polar equation of two cardioids r=1+sinθ,r=1-cosθ. To find the points of…

Q: Find the parametrization for the curve  the lower half of the curve x+3=y^2

A:

Q: A Show that the curve F(t) = lies in a plane.

A:

Q: draw the slope field for y' = x² – y², then use it to sketch three solution curves. %|

A:

Q: What does the gradient vector of a function represent? Create your own real-life example that…

A: