Find the equation of the tangent plane to the graph of (x, y) = In (16x? – 13y²) at the point (1, 1). (Use symbolic notation and fractions where needed. Enter your answer using x-, y-, z-coordinates.) the equation: z= 32x – 26y + 58

Q: 7. Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass…

A: Given a function of the curve, y=ax4+bx3+cx2+dx+e To find the coefficient a,b,c, and d such that the…

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

A: Given that   f(x,y)= z = x2-2xy+y2     So,  this can be rearrange as…

Q: Find the tangent plane to the equation z = 6e* – 2y at the point (4,8,6) - II

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Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

A: Given: x=et……1y=te-t……2 where t≥0   To find: Slope of line tangent at x=3

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: Find the tangent/s as directed to the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x –…

A: The objective is to find the equation of tangent line to the parabola x+2y2+2x-y-3=0 which is…

Q: - 6y Find the tangent plane to the equation z at the point (12,24,4) z =

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Q: Find the tangent/s as directed:to the parabola (x + 2y)^2 + 2x – y – 3 = 0, parallel to the line x –…

A: Given equation of line is  x-4y=24y=x-2 y=14x-12 So comparing with the slope equation formula,…

Q: Find the general equation of the tangent plane to the surface x2 + y2 −2xy −x + 3yz = −4 at the…

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Q: 1. Find the equation of the tangent plane to the given surface at the point (0,-1,-2). * 2r2 „2

A: by using formula of plane

Q: Find an equation of the tangent plane to the surface at the given point. z = x2 - 2xy + y2,  (2, 3,…

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Q: Find the points on the curve a = ť² – 14t – 9, y =t² + 14t + 1 that have: | A. a horizontal tangent…

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Q: Find the equations of the tangent line in the given plane. Tangent to the parabola z = x² + 3y² , x…

A: Tangent line equation problem....

Q: Find the equation for the tangent plane to the surface at the indicated point. -4x – y+ 2z = 1, P(1,…

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Q: Find the equation of the tangent plane to the surface - 8x3 + 7y³ + 3xy at the point (2,0, 64).

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Q: Find the rightward-pointing (positive x-direction) unit tangent to the curve P = {(x, y) E R² |y =…

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Q: Find the tangent plane to the equation z = - 32² – y² + 3y at the point ( – 5, 3, – 75)

A: z=-3x2-y2+3y  and the point (-5,3,-75)

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

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Q: Find the tangent plane to the equation z = 2x – 3y + y at the point (1, 2, – 8). -

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Q: Find the equation of the tangent plane to the surface z = 4 号+ゾ + y² at the point (2, -3, 10)

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

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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,…

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Q: Find the equation of the tangent plane to z = e + x + x³ + 9 at the point (2, 0, 20). z =

A: According to question We have to calculate the equation of the tangent plane .

Q: ind the equations of the tangent line to the ellipse x² + 4y² + z² = 9, x = 2 at the point (2, -1,…

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Q: Find the tangent/sto the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x – 4y = 2.

A: The equation of the parabola is given as  x+2y2+2x-y-3=0. On simplifying,…

Q: Find the tangent plane to the equation z = 3e²²-2y at the point (4, 8, 3)

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Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the…

A: Given" Parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = x − 1 at…

Q: Find the tangent plane to the equation z 5a2 - 4y +5y at the point (5, 5, - 200)

A: The equation of the tangent plane to a surface  is given by fx(x-a)+fy(y-b)+fz(z-c)=0where (a,b,c) =…

Q: Given the function z = = f(x,y) = 2y³ -5xy-3x²+2, find the equation of the tangent plane at (1,-1),…

A: Given problem:- Given the function z  = f(x, y) = 2y³ −5xy-3x²+2, find the equation of the tangent…

Q: Find the tangent plane to the equation z = 6e" -20 at the point (4, 8, 6)

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Q: Find the equation of the plane tangent Z = (x+2)*- (y-1)²-5 at (2,3,3) to

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Q: Find the tangent plane to the equation z 5z° + 4y – y at the point (4, 2, – 66)

A: Given: z=-5x2+4y2-y      4,2,-66

Q: Find c so that the line y = 4x + 3 is tangent to the curve y= x^2 + c?

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Q: Find the equation of the plane in the figure, which is tangent to the graph f(x, y) = 0.2x* + 0.8yº…

A: We have to find the equation of the plane in the figure, which is tangent to the graph.

Q: The x- coordinate of the point on the graph of y = Vx-1 at which the tangent line is perpendicular…

A: slope of tangent of the curve y=x-1 is dydx=12x-1 slope at (x1, y1)dydx=12x1-1=m1if (x1, y1) is the…

Q: Find the tangent plane to the equation z 5x? – 2y? – 5y at the point (3, 0, 45).

A: We need to find the tangent plane equation at (3,0,45)

Q: Find the tangent plane to the equation z = 3x2 + 4y? – y at the point (3,5,68)

A: We have to find the tangent plane equation to the given surface at a given point.

Q: Find the equation for the tangent plane and the normal line at the point Po(2,3,1) on the surface 3x…

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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 the tangent plane to the equation z 4e- 4y at the point (8, 16, 4)

A: Let x0,y0,z0=8,16,4 be a point on the given surface. Then, the equation of tangent is…

Q: Find the equation of the tangent plane to z = e9 +x + x³ + 6 at the point (3, 0, 253).

A:

Q: Find an equation of the tangent plane to the surface at the given point. z = x2 + y2 + 4, (1,2, 9)

A: We know that the equation of tangent plane to the curve z=f(x,y) at point (a,b,c) is

Q: Find the equation of the tangent plane to the surface -2² at the point y = 2x2 – (0, –1,2)

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Q: Find an equation of the tangent plane to the surface at the given point. 4x2 + 2y2 + 5z2 = 177, P =…

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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 an equation of the parabola y = ax² + bx + c that passes through (0, 1) and is tangent to the…

A:

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

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Q: Find an equation for the tangent plane to z = 9x? – 8y² at the point (1, 1, 1). - = 0.

A: Here we find the equation of tangent plane.