a) Find the derivative of f(x, y) = xe* + cos(xy) at the point (2,0) in the direction of V = 3i – 4j.

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 equation of the line tangent to the curve xy^3+xy=6 at the point (3,1). When the equation…

A: Firstly, we will find derivative And then we can solve for y'and we get

Q: Find an equation of the tangent line to the curve 2(z² + y°)² = 25(æ² – y³) (a lemniscate) at the…

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Q: Show that an equation of the tangent line to the graph of =D2 at the point (a, b) is given by 2. b…

A: It is given that, Now take the derivative of the given function with respect to 'x'. Therefore,…

Q: Determine the equation of the tangent line and the quadratic approximation to the function z = e2"…

A: Given function is: z=e2x To find the equation of the tangent at a point x=x0 to curve y=fx,…

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: Find the equation of the tangent line to the curve y=2sin(x) at the point (pi/6, 1) in y=mx+b

A: Using equation of tangent formula.

Q: 2. Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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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: Find an equation of the tangent to the curve given by tan(0), y = sec(0) at the point (x, y) = (1,…

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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: Find an equation of the tangent line to the curve y = 2x sin x at the point (, n) O A. y = -2x O B.…

A: According to our guidelines, we can answer only one question, other questions can be reposted.

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: at the point corresponding to the given value of the parameter. x = esqrt t,  y = t − ln(t4),  t =

A: Answer : we have to find the equation of the tangent.                 for this e have to calculate…

Q: Find an equation of the tangent plane at the given point. f (x, y) = sech(x − y),  (ln 4, ln 2)

A: The given surface is, fx,y=sechx-y. At the point, ln 4, ln 2. The equation of the tangent plane to…

Q: What is the equation of the line tangent to the curve e" + cos(x) = 1 at the point (6,0)? A y = x -…

A: Given, The equation of the curve ey+cosx = 1 We have to find the equation of the line tangent at the…

Q: Find the slope and the equation of the tangent line to the given curve at the point corresponding to…

A: The solution are next step

Q: Find the equation of the line tangent to the curve y = cos(2x) at the point where 3

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Q: Find an equation of the tangent plane at the given point. f (x, y) = x/√y,  (4, 4)

A: Given : The function is f ( x, y) = xy and point ( 4, 4 ).

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 line to the curve y = 6x cos x at the point (7, The equation of…

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Q: Find the equation of the tangent line to the curve y= fa)=cos&) at the point a,)

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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: At the given point, find the line that is tangent to the curve. 5x3y - n cos y = 6t, tangent at (1,…

A: 5x2y-πcosy=6π=ddx(5x2y-πcosy)=ddx(6π)=10xy+5x2y'+πy'siny=0=(5x2+πsiny)y'=-10xy y'=-10xy5x2+πsiny…

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: Find the equation of the tangent line to the curve y = 6 sin x at the point (T/6, 3).

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Q: Find the equation of the tangent line of the curve y = sin x + cos x at the point A ( π ,√2 ) .…

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Q: 1. (a) Use implicit differentiation to find the slope of the tangent to the curve y? – xy +y + 2 = 0…

A: Given: The equation of the curve y2-xy+y+2=0

Q: Q3. Find the equation of the tangent line of the curve y= sinz + cos z at the point A(-, V2).

A: The given curve is y=sin x+cos x and at the point is Aπ4, 2  To find the equation of the tangent the…

Q: What is the equation of the line tangent to the curve e + cos(x) = 1 at the point ,0|? y=x+ y=0 TT…

A: Given that the curve is ey+cosx=1 and the point is π2,0. It is required to find the equation of…

Q: Find the equation of the tangent line at the point (−2,2) to the curve defined implicitly below. 4y2…

A: We have to  find tangent line to curve at given point at (-2,2).Cirve equation is given by:

Q: Find an equation for the tangent line to y=f(x) and the specified point Answer in y=mx+b form

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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: Find the equation of the tangent line to the curve y = 4x cos x at the point (, - 4). The equation…

A: We can answer the question in the following steps.

Q: Find an equation of the tangent plane at the given point. g(x, y) = ely, (4, 1) (Express numbore in

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Q: II. Find the equation of the tangent line to the curve z2+V#j+y² = 19 at the point (1, 4).

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Q: (2.;v3). 1 Find the equation of the tangent line to x? +y²: = 1 at Use exact values in y = mx + b…

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Q: Show that th equation of the tangent to the curve X 1승 +1-2(a 0,b + 0) at the point (a,.b) is 즈+-2 X…

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Q: Find the equation of the tangent line to the curve y = 8 sin z at the point (, 4). 6

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Q: Find the equation of the tangent line to the curve y = 4x cos x at the point (, - 4). The equation…

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Q: Find the slope of the tangent to Ax) = x²e* at the point (1, e). a) e b) 1 c) 3e d) 2 + e

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Q: - Find an equation of the tangent line to the curve sin(r+y) = 2y – 21 at the given point (-7, –x).

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Q: ) Find the equation of the tangent line to the curve y = 2x cos x at the point (π,-2π). The equation…

A: we have to find tangent to f(c) at x=pi

Q: Find an equation for the tangent line to the parabola y x*at the point P(1, 1). %3D

A: Given,            The parabola is y=x2 and the point is P1,1.We know that,            The equation…

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

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Q: Find the equation of the tangent plane to the graph of xe*y- eyz = In(x?) at the point (1,1).

A: Solution

Q: Find the equation of the tangent line to the curve y 6x cos x at the point (π, = The equation of…

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Q: Determine the equation of the curve whose tangent line at any point (x, y) is e* - cos x and passes…

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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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Q: Find the equation of the tangent line of the curve y = sin x + cos x at the point A(, v2). 4'

A: Point-Slope form of equation of line : y-y1 = mx-x1 where m is the slope of the line and x1, y1 is…