Question

Find the equations of the tangent and normal to the curve
x^{2} + y^{2}+3xy-11 = 0 at the point x = 1, y =
2.

Answer #1

What are the equations of the tangent and normal lines to the
following curve: y2+y+x =
arctan2(sin3(x)) at point (0,-1) Remember
that (arctan (u)=tan-1(u))

What are the equations of the tangent and normal lines to the
following curve:
y2+y+x=arctan2(sin3(x)) at
point (0,1)
Remember that (arctan (u)=tan-1(u))

Find a set of parametric equations for the tangent line to the
curve of intersection of the surfaces at the given point. (Enter
your answers as a comma-separated list of equations.)
z = x2 +
y2, z = 9 −
y, (3, −1, 10)

Find the equations for the tangent line and the normal line to
the curve x = sin^2 (xy)? at point ((1/2),(pi/2)).

Find the slope of the tangent line to the cuve sqrt(7x+y) +
sqrt(3xy) = 11 at the point (3,4).
The slope of the tangent line to the curve at the given point
is:

Use implicit differentiation to find an equation of the tangent
line to the curve at the given point.
x2+y2=(2x2+4y2-x)2
(0, 0.25)
(cardioid)
y=?

Find parametric equations for the tangent line to the curve with
the given parametric equations at the specified point.
x =
e−5t
cos(5t), y =
e−5t
sin(5t), z =
e−5t; (1, 0, 1)

Find parametric equations for the tangent line to the curve with
the given parametric equations at the specified point.
x =
e−8t
cos(8t), y =
e−8t
sin(8t), z =
e−8t; (1, 0, 1)

Use implicit differentiation to find an equation of the tangent
line to the curve at the given point. 3(x2 + y2)2 = 25(x2 − y2) (2,
1) (lemniscate) y= ?

Determine an equation of the plane tangent to the surface
x2 - 3x + y2 - y + z2 + 2 = 0 at
the point (2, 1, 0).

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