Question

Find the equation of the tangent line to the curve

r = 2 sin θ + cos θ

at the point

( x 0 , y 0 ) = ( − 1 , 3 )

Answer #1

Find an equation of the tangent line to the curve at the given
point. A) y = 6x + 3 cos x, P = (0, 3) B)y = 8 x cos x P = \(pi ,
-8 pi)
B)Find an equation of the tangent line to the curve at the given
point.
y = 8 x cos x
C)
If H(θ) = θ cos θ, find H'(θ) and H''(θ).
find H'(
θ)
and H"(θ)

4)
Consider the polar curve r=e2theta
a) Find the parametric equations x = f(θ), y =
g(θ) for this curve.
b) Find the slope of the line tangent to this curve when
θ=π.
6)
a)Suppose r(t) = < cos(3t), sin(3t),4t
>.
Find the equation of the tangent line to r(t)
at the point (-1, 0, 4pi).
b) Find a vector orthogonal to the plane through the points P
(1, 1, 1), Q(2, 0, 3), and R(1, 1, 2) and the...

Find an equation of the tangent to the curve at the point
corresponding to the given value of the parameter.
x = cos(θ) +
sin(4θ), y =
sin(θ) +
cos(4θ); θ = 0

1. Find the equation of the tangent line to the graph of ?2? −
5??2 + 6 = 0 at (3,1).
2.. Find the equation of the normal line to the graph of sin(??) =
? at the point (?/2 ,1).
3.. Find the equation of the tangent line to the graph of cos(??) =
? at the point (0.1)
Find implicit differentiation of dy/dx
a) xy=x+y
b) xcosy=y
c)x^3 +y^2=0

Let r = sin 3θ. Find the equation of the tangent line at θ =
π⁄6.

Find an equation for the line tangent to the following curve at
the point (4,1).
1−y=sin(x+y^(2)−5)
Use symbolic notation and fractions where needed. Express the
equation of the tangent line in terms of y
and x.
equation:

Find an equation of the tangent line to the curve at the given
point.
1.) y= sqrt(5x+ 9), at x= 10.
2.) y= cos(x) + cos^3(x), at x=π/6.

Find the equation (in terms of x and y) of the tangent line to
the curve r=2sin3θ at θ=π/3

Find the slope of the tangent line at each given polar curve at
each point specified by the values of θ.
r = 8 − sin(θ)
r = 1/θ
r = 9 + 4 cos(θ)
θ = π/3
θ = π
Thank you!

Use implicit differentiation to find an equation of the line
tangent to the curve sin(x+y)=2x-y at the point (pi,2\pi )

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