(5) Find the most general function f(t) so that the curve F(t) =, shall lie in a plane.

Q: Find all points (x, y) on the graph of g(x) = x3/3 -3x2/2+1 tangent lines parallel to the line 8x -…

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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: 7-The tangent of the curve x^2+y^2- 2xy3D0 at the point (1,1), is * O a. y=2-x. O b. y=x-2. C.…

A: We find equation of tangent to the curve

Q: FIND THE LENGTH OF THE CURVE y = In sec X from X = 0 to X = - 4

A: Given curve is y= lnsecx .  We have to find the length of the curve from x=0 to x=π4. Length formula…

Q: Prove that the curves y=f(x),(f(x)>0) and y = f (x)sin x, where f(x) is differentiability function,…

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

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Q: Find the orthogonal trajectories of the family of curve y = 3x+c,where c is an arbitrary constant.

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Q: Find the equation of the tangent line to the curve f(æ)= 2x2 – x at x = 1. O T(x) =2+ 3(x – 1) O…

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Q: Find the orthogonal trajectories of the curve x^(2) + y^(2) = c^(2)

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Q: (6) Find the orthogonal trajectories of the family of curves r= 2C cos 0, where C being parameter.

A: Consider the given curve. r=2Ccosθ          (1) Find the derivative of the given equation.…

Q: x = e' and y = te %3D

A:

Q: Find the orthogonal trajectories of the family of curves xy = a where a ≠ 0is an arbitrary constant.

A: Consider the equation: xy=Cy=Cxy'=-Cx2 Substitute the value of C in the first derivative:…

Q: 16 12. Find the coordinates of the points on the curve y = 8 - 3- where the gradient of the tangent…

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Q: *(x, y) = xe"

A:

Q: (6) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

A: Orthogonal trajectory curve of a family of curve is defined as a curve which intersects every member…

Q: Find the orthogonal trajectories of the family of curves x when 'a' is the parameter. +y Da

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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 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: f the line tangent to the graph of y =x* – 2x + 1 at x =-1

A: Idea: find the slope of tangent line by differentiation at x=-1 .then find the point on the curve.…

Q: Find the equation of the tangent line to the graph of the function f (z) = (2+7) (z – 3) at the…

A:

Q: 4. Find the orthogonal trajectories of the family of curves y=Ce*™ +10

A: We have to find the orthogonal trajectories of the family of curves

Q: Find the equation of the tangent line drawn to the curve y - 4x* – 6xy = 0 at the point (-1,3).…

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Q: What does it mean for the differentiability of a function if only one of the Cauchy-Reimann…

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Q: The tangent plane to the graph of the function :==3y+1=(1+y} at the point (1; 1; 3/2) contains point…

A: The given equation of the surface is z=x2y+1. Rearranging the above equation gives, w=z-x2y-1 Find…

Q: What does it mean for the differentiability of a function if the Cauchy-Reimann equations (Ux = Vy…

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

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Q: y6 = C (x² + 1) %3D

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Q: Find the equation of the tangent plane to the graph of the curve f(x, y) = x² + y² at the point…

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Q: Find the equation of the tangent line to the graph of the function f (z) = (z² + 10) (z – 2) at the…

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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: 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: 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: 4. Determine the constant a,b, c, and d so that the curve defined by f(x) = ax³ + bx² + cx + d has a…

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Q: Riemann sits on the line normal to the curve y=x2 -3x+2 at x = 1

A: Given           y=x²-3x+2 and x=1  Slope of the curve is given by =dy/dx

Q: Find the orthogonal trajectories of the family of curves x3y-xy3=c where c is constant

A:

Q: 7. Let f(x,y) = x²y+ry. Find an equation of the tangent plane to the graph of f at the point…

A: The detailed solution is given below Thank you

Q: (6) Find the orthogonal trajectories of the family of curves r= 5C cos 8, where C being parameter.

A: we have to find the orthogonal trajectory for the given function

Q: Suppose f(5) = 2, f'(5) = 8, and g(x) = In [f(x)+4]. Find an %3D equation of the tangent line to…

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Q: Find an equation of the tangent plane at the given point. z = In(x-2y), (3,1,0)

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Q: (2) Find an equation for the tangent plane to the graph of z = where z = f(x, y) is implicitly…

A: Given: The function is fx,y,z=xy+xz+yz-lnz2+1-4. Calculation: Obtain thethe value of  fxx,y, fyx,y…

Q: 7-The tangent of the curve x^2+y^2- 2XY3D0 at the point (1,1), is *

A: Given,           The curve is x2+y2-2xy=0 at the point 1,1.

Q: 7. Find all points (x, y) where the curve y = xe has a horizontal tangent line. 2

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Q: (6) Find the orthogonal trajectories of the family of curves r= 2C sin 0, where C being parameter.

A: See the detailed solution below.

Q: Find the orthogonal trajectories of the given family of curves x^2 + y^2 = c^2. *

A: Curves:  x²+y²=c²

Q: 1. Use implicit differentiation to find all points on the graph of y3 – 3y = 2² + 3r +2 at which the…

A: When tangent is vertical then slope of tangent not defined

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.