Find vectors of the Frenet frame of the curve at any point of
the curve x = a(t − sin t), y = a(1 − cos t), z = 4a cos t , where
a is a positive constant
a.)
Find the shortest distance from the point (0,1,2) to any point
on the plane x - 2y +z = 2 by finding the function to optimize,
finding its critical points and test for extreme values using the
second derivative test.
b.)
Write the point on the plane whose distance to the point (0,1,2)
is the shortest distance found in part a) above. All the work
necessary to identify this point would be in part a). You just need
to...
Find the equation of the tangent line to the curve
y=5sec(x)−10cos(x) at the point (π/3,5). Write your answer in the
form y=mx+b where m is the slope and b is the y-intercept.
A) Find the equation of the curve with slope 4x^2/x^2+1 and
passes through the point (1,0)
B)Find the equation of the curve with slope 4x/ x-5 and passes
through the point (6,0)
C) Find the equation of the curve that satisfies dy/dx = 4x^3y
and whose y-intercept is 19
D) Find the equation of the curve that passes through the point
(1,1) and whose slope at (x,y) is y^2/x^3
Find the equation of the tangent line to the curve at the point
corresponding to the given value of t
1. x=cost+tsint, y=sint-tcost t=7pi/4
2. x=cost+tsint, y=sint-tcost t=3pi/4?