Ql. (a) Sketch the contour plot of f(x.v)=2 using the level curves of height k = -2, -1, 0, 1, 2. 1-x' - y' exist? Lt (b) Does

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 - 2xy + y²,…

A: Equation of tangent plane :  Fx(x-x0) + Fy(y-y0) -(z-z0) = 0

Q: nd an equation of the tangent plane to the given surface at the specified point. z = 4x² - y² + 4y,…

A: Topic:- application of derivatives

Q: (b) Compute the slope of the line that is parallel to the xz-plane and tangent to the surface z = x…

A: Given: Let's calculate the slope of the line tangent to the surface z=x(x+y) at the point that is…

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 – 2xy + y²,…

A: Given: f(x,y)=x2-2xy+y2, (5,7,4).

Q: Find the exact length of the curve. y = In(sec(x)), Osxs n/4

A:

Q: Q.1. Justify why the level curves very close to the origin (0, 0) for the function f(r, y) =…

A: To find the level curves, equate the function fx,y with a constant C.

Q: Given a surface f(x,y) = 0x + (4)y. Find the derivative in the direction of v = at the point (6,…

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Q: Given a surface f(x,y) = -3x + (-1)y. Find the derivative in the direction of v = at the point (2,…

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Q: Find an equation of the tangent plane at the given point. f (x, y) = x^2y + xy^3,  (2, 1)

A: To Find an equation of the tangent plane at the given point. f (x, y) = x^2y + xy^3,  (2, 1)

Q: Q: Find the equation of the tangent plane to the surface:- z-Ln(xj) -x5J , atthe poit (7,4)

A: The given surface is z=lnx2y-xy=fx,y at the point -12, 4. The equation of tangent plane is…

Q: Given a surface f(x,y) = -1x + (2)y. Find the derivative in the direction of v = at the point (6,…

A: The given function is: f(x,y)=-x2+2y2 So, ∇f=∂f∂xi+∂f∂yj     =-2x i+4y j∇f(6,8)=-2(6) i+4(8) j…

Q: Find an equation for the line tangent to the curve x= 2sin(t), y= 4cos(t) at the point defined by…

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: Given a surface f(x,y) = -3x + (4)y². Find the derivative in the direction of v = at the point (6,…

A:

Q: Find an equation of the tangent plane to the surface at the given point. 2 x2 + 2z?ey - x = 33, P =…

A:

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² - 2xy + y²,…

A:

Q: Find an equation of the tangent plane to the surface at the given point.   z= y/1+6x…

A:

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: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² – 2xy + y²,…

A:

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 - 2xy + y2,…

A: This question is based on finding equation of tangent plane.

Q: e tangent line to the ellipse 25 = 1 at the point (x, y). 9. %3D s where the slope is not defined?…

A:

Q: The curves y = In x and y = 3x² have parallel tangent lines at x = A) ± √/ B) C) √6 E) 2

A: Two lines have parallel tangent if slop at the point is same.

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan Y. (4, 0,…

A:

Q: Given a surface f(x,y) = -2x² + (5)y². Find the derivative in the direction of v = at the point (7,…

A:

Q: Q4] Find the equation of the tangent plane and normal line to the surface z + 8 = x e' cos z at…

A:

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan , (7,0, 0)

A:

Q: Below is a plot of a cardioid, which consists of points satisfying x² + y² = (2x² + 2y² - x)² 0.6…

A:

Q: Find an equation of the tangent plane to the surface at the given point. 6. f(x,y) = x² – 2xy + y²,…

A: fx, y=x2-2xy+y2,    1, 2, 1. Partially differentiating with respect to x, we get fxx,…

Q: Justify why the level curves very close to the origin (0,0) for the function f(z, y) = (1-z)(1 – )…

A: As per the instruction, we will be solving the first question. For (1), We are given the function as…

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = (1, 5, 5)

A: Follow the procedure given below.

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

A:

Q: Find the exact length of the curve. y = In(sec(x)), 0 <x< a/6

A:

Q: Find the angle between the curve 2y=e-x/2 and y-axis

A: we will see in next step

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 - 2xy + y?,…

A:

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = L, (1, 2, 2)

A: This is a problem of vector calculus.

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: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 – 2xy + y2,…

A:

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan y/x ,…

A: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan(y/x).…

Q: Find the exact length of the curve. y = In(sec(x)), Osxs- 6

A:

Q: Given a surface f(x,y) = -3x² + (3)y². Find the derivative in the direction of v = at the point (5,…

A:

Q: The parametric equations of a curve are given by x = In (Vi +1) and y = cosh (2t). dy Find the…

A: Use chain rule of differentiation to solve this problem.

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (4, 0,…

A:

Q: (a) Sketch the contour plot of f(x, y)= Y using the level curves of height k = -2, -1, 0, 1, 2. X…

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Q: The curve y = sin'x has a slope of %3D Select one: a. at æ = ± O b. Never O c. at x = 0

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = = arctan 2, (9,…

A: Follow the procedure given below.

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

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² – 2xy + y²,…

A: As we know that the equation of the tangent plane is: nxx-x0+nyy-y0+nzz-z0=0 Where; n→=nxi+nyj+nzk…

Q: Consider the two graphs y= 2x and x2 - xy + 2y = 28. The absolute value of the tangent of the angle…

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Q: 7.) Find an equation of the tangent plane to the surface, x y(2z-3), at the point P(4,4,2)

A: