10. If the curves f(x, y) = 0, y, z) = 0 touch, show that at the point of contact, dr dø dr dø dy dx дх ду

Q: Find the equation for the tangent plane at the point Po = (1,2, 2) on the surface x + 4y2 + 22 = 25.…

A: Equation of the Surface x2+4y2+2z2=25 point 1,2,2

Q: Find an equation for the tangent plane to the surface 22 – xy? = 0 at the point (1, 3, 3).

A: Given that At point (1,3,3) Take, Now to find the divergence of f, The divergence at point…

Q: Find the curvature and radius of curvature of the plane curve at the given value of x.

A: We have,   It is known that radius of curvature is given as, Here K is curvature of the curve.…

Q: 5. Trace the curve r = sinocos³o.

A: Given curve: r=12sinθ cos3θ

Q: Find the angle of inclination 0 of the tangent plane to the surface at the given point. x² + y² =…

A:

Q: (b) Find the circle of curvature at (0, 1)of the curve y = x3 + 2x² + x +1

A:

Q: 7. Find the radius of curvature of the curve y = In sin x at x= r/2 .

A: the formula used to find the radius of curvature is  K=|y''|1+y'23/2                       (1)R=1K

Q: 4. Prove that the following curves are intersecting with a right angle: 5y-2x+y-xy= 0 2y+5x+x-x'y² =…

A: Find your answer below

Q: Find the exact length of the curve. y =  3 +1/2 Cosh 2x,   0≤ x ≤ 1

A:

Q: d'y Consider the curve y = ry+ 1, What is the value of at (0, 1)? dz

A: Given curvey2=xy+1

Q: Find the angle of inclination of the tangent plane to the surface at the given point. x² + y² = 5,…

A:

Q: 4 Find the curvature k of the plane curve y = x +- at x = 1. K =

A: Given curve is , y= x + 4x  at x=1

Q: Find the slope of the tangent line to the curves cut from the surface z= 3x? +4y? -6 by planes…

A: The solution are next step

Q: 2. Find the length of arc of the curve x = + from the point where y = 1 to the point where y = 2. yª…

A: Explanation of the answer is as follows

Q: 16 6xy ds, where C is the right half of the circle x² + y² = 4. Evaluate the line integral

A:

Q: 3. Find the radius and center of curvature of the parabola y=x²-4x+4 at any point (x,y)on the curve.

A:

Q: The equation of the tangent plane at the point P(1, 1,-1) on the surface z = f(x, y) = 4 - -* is x +…

A: As per bartleby guidelines we are supposed to answer only one question per post. This post contains…

Q: |d?y |dx2 K($) = Cos3 %3D

A: Given curve y=f(x)

Q: Find equations for the a) tangent line and b) normal plane to the curve made by the intersection of…

A: Given The given surfaces are 3x2y+y2z=-2 and 2xz-x2y=3.  The given point is 1,-1,1.

Q: 4. Find the radius and center of curvature of the curve y=6x-x³ at the point (1,5).

A: This question is based on radius and centre of curvature formula.

Q: What is the equation for the tangent plane to the surface z = 4x°y2 + 2y - 2 at the point P(1, -2,…

A:

Q: 4) Find the families of lines of curvature of the surface z = r + y? .

A: Given: z=x2+y2

Q: Find the curvature of the curve defined by the function y=3x^2 - 2x + 4 at the point x=2

A: Curvature is defined as : K(x) = |y"(x)| / {1 + [y'(x)]^2}^(3/2).  Note that :- |y"(x)| means the…

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: 5. Are there any points on the graph of x2 - y? – 22 = 1 where the tangent plane is parallel to the…

A:

Q: 13. Find an equation for the tangent plane and the normal line to the surface x? + 2y? - 3z? = 3, at…

A:

Q: What is not true about the curve y = Intersect the x-axis at (2,0). None of the Choices as x ∞, y →…

A:

Q: 15. y= 2x +3 at x = 27

A:

Q: Find reparametri zations two Curve aLt)=(t, Cosht, o, teR.

A: The general form of the parametric equation of the curve in three dimensional space is given by…

Q: Find the equation of the tangent line to the curve y = et at the point (0, 1). Give your answer in…

A: Given,            The curve is y=exx2+1 and the point is 0,1.To find : Find the equation of the…

Q: 7. Find the equation of the tangent plane to the surface: x +y² -z² 1 z, at (2, 1, 2)

A:

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

A:

Q: 4) Find the families of lines of curvature of the surface :=r+y

A: The answer is given in handwritten format --

Q: 2) Find and sketch the circle of curvature at the point on the curve y = x² where the tangent line…

A:

Q: If L is the tangent line to the curve 7 (t)= (2t-1, t, t-2) at (3, 4, 2) and the point where L…

A:

Q: 99. Determine the concavity of the curve x= 2t + In t, y = 21 – In t. %3D

A:

Q: 1. Find the are length of the curve x = (y + 2)2 from y-0 to y=1

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: IFind the exact length of the curve x= 3t -t, y=3t² ,0<t<2 ||

A: We have to find the exact length of the curve. The length of the curve is given by

Q: s to the curve y = x* at the %3D

A:

Q: py*(1 + x*)dx + 2ytan xdy ,where C is closed curve xi +yi = 1

A:

Q: Find the slope of the tangent line to the curve that is the intersection of the surface z=x² - y…

A: The details solution is given below

Q: find length of い) ylm) = bzn Curves 4ょ2..33 + 21 ci) =12 at

A:

Q: What is the equation of the plane that is tangent to the graph of z = x coS y – ye“, when (x, y) =…

A: Equation of the plane tangent to the surface z=f(x,y) :               Let   F(x,y,z) =0 ,then…

Q: 2) Find and sketch the circle of curvature at the point on the curve y x where the tangent line has…

A:

Q: 2) Find the cartesian eauation for the olar curve r=tan e sece ×ニy )yニxと 2.

A:

Q: 23/ Find the angle between two curves: 3 y = 2 - x² , y = x²

A: The angle between two curves is given by the formula tan θ=f2'x0-f1'x01+f1'x0f2'x0 Given,…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.