2. Find the equation of the tangent plane and the normal line at the point (0 ,1 , 2) on the surface cos(7X)–x²y+e² +yz = 4.

Q: In Exercises 1–5, find equations for the (a) tangent plane and (b) normal line at the point P0 on…

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Find an equation for the tangent plane to cos(rx) – x²y+ e*z + yz = -4 at the point (0, 1, –6). = 0.…

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Q: Write the differential dw in terms of the differentials of the independent variables. w = f(x,y,z) =…

A: Hair we have to find out the differentials

Q: Sketch the level curve corresponding to c = 0 for the function given by           f(x, y) = y − sin…

A: We have given the function; f(x, y) = y − sin x This can be written as; z=y − sin x

Q: Q9. Find the equation of the tangent plane to f(x, y) = x ln(y) +x²y+3 at the point (x, y) = (2, 1).…

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Q: 1. Let f(x, y) = -x2 – xy³ + 7. Find an equation for the plane tangent to f at (3, 2).

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Q: Find an equation of the tangent plane to R(u, v) = (e" sin u , eº cos u , e¯-" ) at the point where…

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Q: integrate ƒ over the given curve. ƒ(x, y) = x3>y, C: y = x2/2, 0 <=x<= 2.

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

A: We will find the equation of tangent plane to the given surface.

Q: Find an equation of the tangent plane to the surface at the given point 1, 1 4 z arctan X Find…

A: To work out the required equations using partial derivatives

Q: The tangent line to the curve r(t) =(t°,t“, t³ ) at the point (1, 1, 1) intersects the æy-plane at a…

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Q: Find equations of (a) the tangent plane and (b) the normal line to the surface 2(x−2)^2 + (y−1)^2 +…

A: Given surface is Firstly, we find all first order partial derivatives At point (3,3,5)

Q: Find the linearization L(x,y) of the function f(x,y) = e 3× cos (9y) at the points (0,0) and 0,

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Q: 1. Give an equation of the tangent plane to the surface z = In(4y – x) at the point (3,1,0). 2. Use…

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

Q: a i.e. an of %3D PROBLEM (10): Find the normal derivative V. %3D (1) 6 = x yz in the direction of…

A: we'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: b) Find equations for the tangent plane and normal line at the point po on the given surface.…

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Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈1 − t^2, 5t, 2t^3〉, t = 2

A: r(t) =(1-t2, 5t, 2t3) at t=2

Q: Compute f cos(Tæ) dæ + 10xy dy, where y is a part of parabola y = 3x? from the point (0,0) to the…

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Q: 7. Find the equation of the tangent plane to each surface at the given point. (a) x? + y? + z² = 14…

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Q: Find and equation of a) the tangent plane and b) the normal line to the given surface at the…

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Q: Find equations for (a) the tangent plane and (b) normal line at the point P on the given surface 1)…

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Q: find the decomposition of a(t) into tangential and normal components at the point indicated, as in…

A: Given: r(t)=(t,cost,sint)t=π2

Q: .: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G (x, y) = x³ y² + y² sin…

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Q: (5) Find the equation of the tangent plane to z = 1² + xy +3y* at r = 1, y = 1.

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Q: Find the equations of (i) the tangent plane and (ii) the normal line to the surface z = excos(y) at…

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Q: Find equations of (a) the tangent plane and (b) the normal line to the given surface at the…

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Q: The value of the line integral S(2xy² dx + 2x?ydy + dz) along a path joining the origin and the…

A: To find the value of line integral  ∫c(2xy2dx+2x2ydy+dz)along the path joining origin and point…

Q: Find the equation for the Tangent Plane on the given surface coS ax – x²y + e*z+ yz = 4 Po(0, 1, 2)

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Q: 4. Let f(x, y) = sin(x²y) + vx + e+y. Find the equation of the tangent plane to the surface z f(x,…

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Q: Consider the closed curve in the xy-plane given by x² + 2x + y* + 4y = 5. dy -(x+1) (a) Show that dx…

A: Given data:   The expression for the given function is x2+2x+y4+4y=5.   (a) Differentiate the above…

Q: 1. Fad the equation of the tangent plane and normal line to the surface z = 2r+y at the point…

A: Given that z=2x2+y2. We need to find the equation of the tangent plane and the normal line to the…

Q: Obtain the integrating factor of the non-exact DE, (2 + ycosx)dx + xcosxdy = 0. a. secx b. cosx c…

A: Integrating factor

Q: Evaluate the line integral. { 4) ( y2 dx + x dy; C is the curve x =t2 - 1, y = 4t, 0 st s 1

A: The given line integral is ∫Cy2 dx + x dy; C is the curve x=t2-1, y=4t, 0≤t≤1

Q: 2. Find an equation for the plane tangent to the surface 3x2 - 4xy+ z2 = 0 at the point (1, 1, 1).…

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Q: Q5: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given…

A: Given that  The equation  cos(πx)-x^2y+e^(xx)+yz=4  Point (0,1,2) To find the equation of the…

Q: 4. Let g(x, y) = e"/v, Find an equation for the tangent plane at (x, y) = (2, 1).

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Q: 1. If F(x, y) = (3+2xy)i + (x² – 3y²)j. Evaluate F. dr, where C is the curve given by r(t) = e'…

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Q: Consider z = Ax + By + D be the tangent plane to f(x, y) = 2x² + 5y³ + 9xy + 9x + 3y at (6,9).What…

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Q: Q5: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given…

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Q: Show that the equation dy/dx=x^2/(1−y^2) is separable, and then find an equation for its integral…

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Q: 3. Evaluate the line integral sin(y) dx + (x cos(y) – sin(y)) dy, where C is the straight line from…

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Q: Q5: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given…

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Q: Consider the following. xy + yz + zx = 17, (1, 1, 8) (a) Find an equation of the tangent plane to…

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Q: Find the equation for (a) the tangent plane and (b) the normal line at the point P. on the surface…

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

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Q: Which of the following give the symmetric equations of the normal line to the surface xy + yz + zx =…

A: Normal to the surface is a line perpendicular to that surface.

Q: Integrate h (x, y. 2) = yzi+xj+xzk over the indicated path: (a) the line segment from (0, 0. 0) to…

A: definite integrate calculus