Find the equation of the tangent plane to the graph of 7y f(x, y) = at the point (4, –1). (Use symbolic notation and fractions where needed. Enter your answer using x- y-, z-coordinates.) the equation:

Q: find an equation for the line in the xy-plane that is tangent to the curve at the point…

A: To find an equation for the line in the xy-plane that is tangent to the curve at the point t = 2…

Q: m Find the equation of the tang ent to the curve ym =1 at the point (x1.y1). m

A: Topic:- application of derivatives

Q: If f(z) 2x2 2x + 3, find f'(-1). %3D 2a2 2x + 3 at the point (- 1, 7) Use this to find the equation…

A: We are given the function f(x)=2x2-2x+3. Now,           f'(x)=2x2-2x+3'       =2x2' -2x' +3'…

Q: Find the derivative using the following information.

A: Equation of tangent to curve g(x) at x=2 is y=-3x+2. Its slope is m=-3. Since slope of tangent to…

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

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Q: Find the slope of the line tangent to the curve at the given point. y = 7 cos x ; x = 4 C. - 7V2 7V2…

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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: Let f(x) = 14x + 11 – 3e. Then the equation of the tangent line to the graph of f() at the point (0,…

A: Given: f(x)=14x+11−3ex The equation of the tangent to the graph f(x) at the point (0,8), is given…

Q: Determine the value(s) of x where the tangent to g(x) = (x + 5)(x2 - 1) is parallel to y = -7x - 8

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

A: Given curves x=2+lnt, y=t2+2 and the point 2,3. The objective is to find an equation of the tangent…

Q: Let f(x) = x* – 2x + 14. Then the equation of the tangent line to the graph of f(x) at the point (1,…

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Q: Use the implicit derivation to find the equation of the line tangent to the curve at the point…

A: Here, the equation of the given curve is: y sin (2x)=x cos(2y)...(1) To use the implicit derivative…

Q: ind the equation of the line tangent to the curve 3x² + 16y² = 192 at the point Mx + K. P= (-4, 3)…

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Q: Let f(x) = 12x + 11 – 15e*. Then the equation of the tangent line to the graph of f(x) at the point…

A: Solving by equation of tangent we have

Q: (b) Find the value of k for which 2y +x k is a tangent to the curve y +4x 20. %3D

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Q: If f(x) = x° – 5x + 1, find f'(1) f'(1) = Use it to find an equation of the tangent line to the…

A: Given function, fx=x3-5x+1 Tangent is passing through (x1,y1) (1,-3).

Q: Find an equation of the tangent plane at the given point: F(r,s)= 2r3(1/s0.5) - 2(1/s4), (2,1)

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Q: Find all points on the graph of x2y − 2x + 63y = 2 where the tangent line is horizontal. (Enter…

A: Differentiate the equation x2y-2x+63y=2 wrt x:  ddxx2y-ddx2x+ddx63y=ddx22xy+x2dydx-2+63dydx=0

Q: Find the equation of the tangent line at x = 2 for f(x) = 4+x-2x²-3x³. Write the answer in the form…

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

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Q: Since the tangent equation of f(x) = x^3 – x^2 + 3x – 5 drawn from the x = 1 apse point on it is y =…

A: Given : Function  f(x) = x3 – x2 + 3x – 5 Tangent equation on the given function f(x) at point x =…

Q: For the function z = = f(x, y) = x² − xy² + y³, find the equations of the tangent lines in both the…

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Q: Find an equation of the tangent plane to the graph of F(r, s) at t F(r. s). - (3r4 1 + 1), (-1, 1.…

A: Introduction: Let z=f(x,y) denote the equation of a surface S in R3, and P=(a,b,c) denotes a point…

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: The tangent line to the graph of y = In(2x) is perpendicular to x + 4y = 1 at the point where…

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Q: Find an equation for the tangent line to the parabola y = x² at the point P(1, 1). A y=2 B) y = x…

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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 = 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: Let f(x) = 4x + 7 – 17e². Then the equation of the tangent line to the graph of f (0, -10) is given…

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Q: Find an equation for the tangent line to the parabola y = x² at the point P(1, 1). A y=2 B) y = x…

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Q: find an equation of the tangent plane at the given point. f (x, y) = x2y + xy3, (2, 1)

A: Let z = f(x, y) is any function and let x0, y0 be a point on f then equation of tangent plane is,…

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: Determine the value of a, given that the line ax+y+1 = 0 is tangent to the graph of y= ax-6x+1 at x…

A: Given  y=ax2-6x+1find derivativey'=ddx(ax2-6x+1)y'=2ax-6+0y'=2ax-6at x = 1y'=2a(1)-6y'=2a-6

Q: Find an equation of the tangent plane to the graph of f(x, y) = 4x² - 7xy² at the point (7, 8). z =

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Q: f(x,y) = x/3 – x/3y² is harmonic? Does the function

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Q: %3D %3D .2 ,2.

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Q: Let f(x) = 6x + 2 – 7e*. Then the equation of the tangent line to the graph of f(x) at the point (0,…

A: Here we find the tangent equation then we find the value of m and b.

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: The Tschirnhausen cubic is the curve given by the equation x2 = y3 + 3y?. At which point(s) (x, y)…

A: Given query is to find the point of horizontal tangent.

Q: Find an equation for the line tangent to the graph of f(x) = 7re %3D at the point (a, f(a)) for a =…

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Q: Find an equation for the tangent plane to the graph of the function f (x, y) = y In(x² + 2y) + xy at…

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

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Q: Find the equation of the tangent line to the function f(x) = 2x? – x at the point where x form y =…

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Q: Let f(x) = 2x + 15 – 7e". Then the equation of the tangent line to the graph of f(x) at the point…

A: We know that equations of tangent line at the point (x1,y1) is given as - ( y - y1 ) = m ( x - x1 ).…

Q: Find the equations of the tangent lines in both the x-direction & the y-direction to the function z…

A: We need to find equation of tangent line.

Q: If y1=2x+4 and y2 =x^2+C, find the value of C such that y2 is tangent to y1

A: Given: y1=2x+4    and    y2 =x²+C   To find :the value of C such that y2 is tangent to y1

Q: x = VE, y = t? – 2t; t = 16

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Q: Find an equation of the tangent plane to the graph of F (r,s) at the given point: F (r,s) =…

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Q: Q2)B/ Find the points on the curves y(X) given by y = x - 6x? + x+3 where the tangents are parallel…

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Q: Find the value of 'a' for which the tangent to the curve ƒ(x) = (a + 2) x³ − 3ax² + 9ax − 1 never…

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