Find the equation – in any convenient form – of the tangent plane to z = x² sin(x+2y) at the point (3, 1). [Please leave all values as exact rather than numerical approximations].

Q: Find the equation of the tangent line to sin (x – 2y) = 2xy – 1 2лу — (1.:) at the point ( 1,

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Q: Find the equations of the tangent line in the given plane. Given: v = (3t - x)e-2t

A: Given function - v = 3t-xe-2tWe need to find ∂2v∂t∂x,Concept - We need to partially differentiate v…

Q: ind the equation for the tangent lin to y- fcx) at the specified point. fcx) where x=1 x2

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Q: Find an equation of the tangent line at the given point on the curve. (a) x = 2 – 3 cos 0, y = 3+ 2…

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Q: Find the equation of the tangent line to sin-(x - 2y) = 2xy – 1 %3D (1). at the point

A: Given,            The equation of the line is sin-1x-2y=2xy-1 and the point is 1,12.We know that,…

Q: Find the equation of the tangent plane to z = ey + x + x2 + 11 at the point (5, 0, 42).

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Q: Find an equation of the tangent plane to the graph of f(x, y) = at the point (2, 9). y Z =

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Q: v = (3t - x)e-2t

A: v=3t-xe-2t Partially differentiating with respect to t, we get…

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: find the tangent line of the curve (1– sin(1).tcos(1)) at the vale t(0) = T, (and so at the point(…

A: The curve is defined by the equations: x(t)=(t-sin(t))    and    y(t)=tcos(t)

Q: Find the equation of the tangent line to the curve given by F(t) = (cos(rt), t, 1+ t²), for t € [0,…

A: (a) First find the derivative of the given curve.  r't=-πsinπt, 1,…

Q: Find the equation of the tangent line of the curve y = sin r + cos a at the point A(, v2).

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Q: f(x) = |x + 1| (-1,0) Prove that has no tangent line at

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Q: Find an equation for the tangent plane to z = cos(x2 + y2) at the point /等,0).

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Q: Find the tangent plane to the equation 3y cos(4x – 2y) at the point (2,4,12) Z =

A: Z=3ycos(4x-2y)  Point= (2,4,12)

Q: Find the equation of the tangent plane to z=e^y+x+x^4+6 at the point (4,0,267).

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Q: a point on the cor ve y=x² - 2x -3 at which is parallel to Find the tangent line the X-axis

A: Given query is to find the the point where tangent line paray to x axis.

Q: Find the equation of the tangent line to the given function at z = a. w(2) = tan (3x) +x, a=0 3 !!

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Q: Find the implicit equation of the tangent plane to z = In(x² + 1) + y² at the point (0, 4, 16).

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

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Q: find an equation of the tangent plane at the given point. f (x, y) = x2 + y−2, (4, 1)

A: To find equation of tangent plane at (4,1)

Q: Find the equation of the tangent plane to z = In(x²y) – x/y at (-;4).

A: Let x0,y0 be any point of surface function z=fx,y. Then the surface has a non vertical plane at…

Q: Find an equation of the tangent plane at the given point: F(r, s) = r²s-0.5 – 2s-4, (-1, 1) z =

A: The formula to find the equation of a tangent plane at a point (a, b) to a given surface f(r,  s) is…

Q: Find the equation of the tangent line to the curvef (x) = -x' + 2x at x = 1. о Тx) 3D 1 + (-1)(х —…

A: To find the equation of tangent line to the curve at x=1

Q: f(x,y) = 4x² + y² + 2 at the point wherex = 1 and y = 1.

A: The equation of the tangent at point (1,1) is: z=f(1,1)+fx(1,1)(x-1)+fy(1,1)(y-1)

Q: Find an equation of the tangent plane to the graph of f (x, y) =2x2 - 4xy 2 at (-1, 2)

A: Given: f(x, y) = 2x2 -4xy2  To find: Equation of tangent plane to the graph of  f(x, y) = 2x2 -4xy2…

Q: Find the equation of the tangent plane to z = ln(x³ + 1) + y³ at the point (0,6,216).

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Q: Find the equation of the tangent line (assuming it exists) to f(x) = x² + x at x = -2. Give your…

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Q: Find the equation for the tangent line to the curve f(x)=cos(x)-2sin(x) at the point (0,1). O y=-x+1…

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Q: Find the equation of the tangent line to the curve at the point (-÷5) (글 given a cos(2 y) = 0. V3 a)…

A: We need to find the equation of the line.

Q: Find the points on the cardioid r = 4(1 – sin0) at which there is a horizontal tangent line, a…

A: According to the given information, it is required to determine the horizontal tangent line,…

Q: The slope of the tangent line to the curve parametrized by the equations x (t) = -2(cos(t) + t…

A: Slope of tangent is equal to dy/dx.

Q: 2y+ In(xy) +z = 6 at the point (4,0.25, 2)

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Q: Find the equation of the tangent plane to z = ey + x + x² + 7 at the point (5, 0, 38). = Z |

A: To find the equation of tangent plane to z=ey+x+x2+7  at the point 5,0,38In general the equation of…

Q: 8. Find a parameterization of the tangent line to r(t) = (cos(t), sin(2t)) at the point

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Q: Find the equation of the tangent plane to z = In(x³ + 1) + yª at the point (0,3, 81).

A: We have to find equation of tangent plane at (0,3,81).

Q: Find the equation of the tangent plane to z = e" + x + x² + 6 at the point (5, 0, 37).

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Q: Find an equation of the tangent plane to the graph of f (x, y) = xy 2 - xy + 3x 3y at P = (l, 3).

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Q: Find an equation for the tangent line to the curve parametrized by x = e³t sin(πt) and y = et at the…

A: x=e3tsin πty=e2t

Q: . Find the slope of the tangent line to sin(z – x) + y° cos.x = y at( А. 4 В. -1 С. О D.

A: This is the final solution of given question.

Q: Find the equation for the tangent plane to the graph of h (x, y) = y sin (x y) + yª + 3 x² at the…

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Q: Find the derivative 4cos4t sin4t O2cot4t O Other: -1/2 cot4t of the parametrically defined curve (t)…

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Q: Find an equation of the tangent plane to the graph of f(x, y) = 9x at the point (2, 9 Vy z =

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Q: The parametric form of the tangent line to the image of f(t) = (5t², 2,t – 2) at t = -1 is L(t) =

A: Topic = Application of derivative

Q: Find an equation for the tangent plane to the graph of f(x, y) V3+ r2 – 3y2 at the point P(2, 1,…

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Q: Find the tangent plane to the equation 3y cos(5x – 4y) at the point (4,5,15)

A: z=3y cos5x-4y Let, Fx,y,z=3y cos5x-4y-z=0  ......(1) Now,  Fx=∂Fx,y,z∂x=-3y sin5x-4yx5-0…

Q: Find the equation of the tangent plane to z = e + x + x² + 4 at the point (3, 0, 17).

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Q: The line y = -4x +b is a tangent line to the curve 3y²r + sin(2y – 4) = /(2y) at (a, 2).

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Q: Find an equation of the tangent line to the curve at the given point by both eliminating the…

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Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.