If ø = 4xy, find x and y components of the velocity at (1, 4) and (4, 4). Calculate the discharge passing between the streamlines passing through the points.

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 the gradient of the curve and the equation of the tangent line at the specified point x*y' -…

A: Given: Curve, x2y3-2xy=6x+y+1; and point 0,-1

Q: If the line y=x+4 is tangent to f(x)=ax2 +bx at the point (2,6), then a+b?

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Q: Find the equation of the tangent plane to 4 = Z = eª + x + x* + 4 at the point (1, 0, 7).

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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: integrate ƒ over the given curve. ƒ(x, y) = x3>y, C: y = x2/2, 0 <=x<= 2.

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Q: Find the equation of the tangent line to the curve 3 x' + 2 y – 22 = 3 xy – x at the point (2, 2).…

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Q: Find the total differential. w = (3x + 4y)/(y + 3z)

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Q: Find the equation of the tangent line to the curve y= x +4 e at the point (0,4). O A. y=4x+5 O B.…

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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: (b) Find the equation of the line normal to the tangent at the point (1,4) on the curve x'y+ xy =…

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Q: Use implicit differentiation to find y' at (3, 0) for 2x + e3zy 55 %3D

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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 derivative of the function at P0 in thedirection of v. ƒ(x, y) = 2xy - 3y2, P0(5, 5), v =…

A: The given function is ƒ(x, y) = 2xy - 3y2. Note that fx=2y    and  fy=2x-6y. at P0=5,5,  fx=10   and…

Q: Find the equation of the tangent line to x? – y + y? = 21 at the point (1,5).

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Q: find the values of the derivatives

A: Given: w=z+z first we differentiate given expression with respect to z then substitute z=4

Q: Find f (3) and f' (3), assuming that the tangent line to y = f (x) at a = 3 has equation y = 5x + 2.

A: Tangent to a function at a point is a line which just touches the graph of the function at that…

Q: Find the equation of the tangent line at (1,2) for x'+2y = 9 y- A= B(x - C)

A: point (1,2)  ; x3+2y2=9 In the given point x is 1, y is 2

Q: Find the slope of the tangent line to the curve1x^2+1xy−3y^3=−24at the point (−2,2).

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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: If y = 4x³ + 2x² + 11, find the approximate value of y when x = 2.01, using differentials.

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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 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 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 derivative of this complex function: where z=x+jy (2+jj?

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Q: Find the differential of the function z=2x'y %3D

A: If z is a function of two variables defined by z=f(x,y) then the differential dz or total…

Q: The equation of the tangent line to Y f(x) at a can be written in the form y 3 = mx + 6 where m =…

A: Given Data: Function: fx=6sinx6sinx+4cosx   Differentiate the function with respect x is,…

Q: The derivative of f(x,y)=9xY at (e,1) in the direction of v=(4,3) is !!

A: TO FIND THE DERIVATIVE i.e DIRECTIONAL DERIVATIVE IN DIRECTION OF V= (4,3) at (e,1) STEPS 1. FIRST…

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: d the equatiom of the tangent line to the curve xy – 7 = Vx + y² at the point (5,2).

A: For finding tangent line to the curve , find the derivative of the function and put the value of…

Q: Find f(3) and f'(3), assuming that the tangent line to y = f(x) at a = 3 has equation y = 5x +2.

A: Consider the provided function, y=5x+2 Find the value of f3  and  f'3 at a=3. y=5x+2 We can write…

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 slope of the line tangent to the x³ – 2x + 1 at x = 2 curve y %3D %3D O-10 O 1/10 O-1/10 O…

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Q: Find an equation of the tangent plane to the graph y = x² + 2xz at (1,3, 1). (Possible Answer: 4r –…

A: We have to find an equation of the tangent plane to the graph y=x2+2xz at 1,3,1.

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: A volleyball is moving 16 m/s at 25o North of straight down. If +x is East, +y is North, and +z is…

A: Draw the sketch, as follows: Since the ball is moving 25° North of "Straight Down" direction, its…

Q: Find an equation of the line tangent to the level curve of the function x 3xy passing through the…

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Q: Express x = ln(7t), y = 9-t in the form y = f(x) by eliminating the parameter.

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Q: find the derivative of the function at P0 in the direction of u. ƒ(x, y) = 2xy - 3y2, P0(5, 5), u =…

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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 the equation of the line tangent to xe' + ye = 1 at the point (0, 1).

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Q: Find the differential of f(x, y) = vx2 + y³ at the point (1,2). df

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Q: Find an equation of the tangent llne to the về at the given poln 6x y = (x + 1)2' (0, 0)

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Q: I attached a picture of the question

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Q: Find the total differential. z = 6x *y5 iz

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Q: Find the equation of the tangent plane to z=6x2+2y2  at the point (1,5)

A: Given  z = 6x2+2y2  at the point (1,5)

Q: Find the equation of the tangent plane to z= 6x +2 at the point (1,5).

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Q: Calculate the equation of the tangent plane to z = at (4, 2) y?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.