Find the point on the graph of f(x) = Vx that is closest to the point (5, 0). (x, y) =

Q: find an equation of the tangent plane at the given point. f (x, y) = ln(4x2 − y2), (1, 1)

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Q: Find the derivative of the function f (x, y) = x²y + y²z: at Po(1,2,3) in the direction of û = 2î –…

A: To find the derivative of the function f(x,y)=x2y+y2z at P0(1,2,3) in the direction of…

Q: . Find an equation of the tangent line y = e* that is parallel to the line x – 4y = 1.

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Q: Find the equation of the tangent and normal line of the function f(x) = V2x – 1 at the point (5, 3).

A: fx = 2x-1     , 5,3f'x = ddx2x-1     = ddx2x-112        = 122x-1ddx2x-1        = 222x-1 = 12x-1∴f'5…

Q: 2. Find the tangent lines to the curve y = x4 – 14x2 + 17x + 40 perpendicular to the line x = 7y +…

A: Given, y=x4-14x2+17x+40 Now differentiate with respect to x we get, dydx=4x3-28x+17 The tangent is…

Q: Find an equation of the tangent plane to the graph of f(x, y) = In(4x² – 2y2) at the point (1, 1). z…

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Q: Find the equation of the tangent line to the curve y2=6x-3 perpendicular to the line x+3y=7

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Q: Find the equation of the tangent plane to the graph of g(x, y) = ln(6x² – 3y²) at the point (1, 1).…

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Q: Calculate the differential of the function y=x5−7x3+5x at the point x=2 when dx=0,2.

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Q: z = Vx4 + yf, fz (1, 2)

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Q: Find the equation of the tangent line to the curve y²(y² – 4) = x² (x² – 5) at the point (0, –2). |

A: Equation of tangent line is given by:y-y1=dydxx=x1·(x-x1)      .............[1]So first find dydx at…

Q: Find the equation of tangent for the implicit function x3 - xy2 + 3y2 + 4 = 0. at the point (1, 2)

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Q: 5. Find the equation of the tangent line on x² + y? = (2x² + 2y² – x)² at (0, ).

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Q: Find all the points on the curve x² y² + 2xy = 3 where the slope of the tangent is -1. O (1,1) O…

A: We have find possible point where the slope of the tangent is -1

Q: The equation of the line tangent to f(x) = (x² – 9) (2x – 1) at æ = 2 is y = 2x –*

A: Given that: f(x)=(x2-9)(2x-1)

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

A: Given the parabola x+2y2+2x-y-3=0..............i  Determine the slope of given line x-4y=2…

Q: Find the linear approximation of the function at the given point. f(x, y) = 4 sinx - 6 cos y at (0,-

A: Given,           The function fx,y=4sinx-6cosy  at  0,π2.

Q: .The line y + 2x = 0 is tangent to y = F(x). Determine F(x) if F(x) = 4x³ + 2.

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Q: Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y-2y³ In the…

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Q: Find an equation of the tangent plane to the graph of f(x, y) = In(4x² – 2y2) at the point (1, 1).

A: To Determine: FInd the equation of tangent plane to the graph of…

Q: Find the derivative of the function f(x, y) = 2x² – y² at the point M = (1, 1) in the direction…

A: We have to find the derivative of the function fx,y=2x2-y2 at the point M=1,1 in the direction…

Q: Find the equation of the line that is tangent to the curve r = x In y, x > 0, at the point (1,е).

A: Equation if the line (y - y1) = m(x -x1) D(uv) = uDv + vDu , where D is the differentiation of…

Q: Consider the function f (x, y) = x²y³ – 3xy³. Compute the value of the derivative frvy at the point…

A: Given function is f(x,y) =  x2y3 - 3xy3 we have to find fxyy at the point (2,1).

Q: Find an equation of the line tangent to y = xsin x at the point x = 1.

A: The given equation is y=xsinx.

Q: Find the derivative of the function at Po in the direction of u. f(x, y) = In( 6 x - 3 y), Po(-7, -4…

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Q: Find the derivative. 8) y =V4x +2 dy dxN4x + 2 =N4x + 2 A) dy В) dx 4 1 N4x + 2 dy C) dx dy D) dx 8…

A: SOLUTION-

Q: Find the equation of the tangent line to the curve y = Vx – 3 at the point (4, 1). - o y = }x - 3 2…

A: Explanation of the answer is as follows

Q: Find the point (x,y), at which the graph of y = 8x+6x-3 has a horizontal tanger The function y= 8x…

A: Our Aim is to find the point (x,y) at which the graph of y=8x2+6x-3-(i)has a horizontal tangent.

Q: Find all points (x, y) on the graph of y = x/(x - 2) with tangent lines perpendicular to the line y…

A: Given:

Q: The tangent line to the curve ³ + y³ = 9xy at the point (4,2) intersects the y-axis at y = -1. -2.…

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Q: Find the point(s) (x, y) on the function f (x) = V1+ 2x where the tangent line is parallel to the…

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Q: 2xy - y² + x = 2 at the point (1,2). - Find the equation of the tangent line to ² +2

A: By using equation of tangent line formula, we find the required tangent line.

Q: find the slope of the curve x = e^-tcost2t, y=e^-2tsin2t at the point t= 0

A: find out the slope of the curve at t=0

Q: Find an equation of the tangent plane to the graph z = Væ + y³ nt (8, 2, 4).

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

Q: Find the derivative of the function at the given point in the direction of A. 3) f(x, y, z) = -10x+…

A: Here initially we need to find out the partial derivative of the given function to find out the…

Q: Find the equation of the tangent plane to the graph of f(x, y) =−3x2 − y3 at the point (x, y) = (2,…

A: The given function is

Q: Find the slope of the line tangent to y = 3x(cos x) at (7/2, 7/2). A) -3/2 B) 3x/2 C) /2 D) -x/2

A: Consider the function  y=3x(cosx) Point : π2,π2

Q: Find a point on the graph where x = t² - 1, y = 2t has a vertical tangent.

A: For vertical tangents dx/dy=0

Q: Find the derivative ofy. with respect to x if y=(Ix +5) (9x² +2x) %3D

A: Given that: y=(x+5)(9x2+2x)

Q: Find all (x,y) points where x² +4y² +4x- 8y+4 = 0 has horizontal or vertical tangent lines.

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Q: find the derivative of the function at P0 in thedirection of v. ƒ(x, y) = 2x2 + y2, P0(-1, 1), v =…

A: Given: fx,y=2x2+y2  We know that, The direction of v is the unit vector obtained by dividing v by…

Q: I attached a picture of the question

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Q: Use differentiation rules to find y′=dy/dx   y = 3 · cos5 ( x − 4/x2 )

A: We apply the power rule then apply the chain rule

Q: The gradient of the tangent to the curve = 4x + y at the point (0, 1) is D - 2

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Q: Use differentiation rules to find y' = dy/dx.

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Q: The total derivative of the function f(x, y) =3x'y- xy is

A: Find the total derivative

Q: Find

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