Find all horizontal and vertical tangent lines for the parametric curve defined by x(t) = t^3...

Find all horizontal and vertical tangent lines for the parametric curve defined by x(t) = t^3 - 3t +1, y(t) = 4t^2 +5. then write our the equations for the tangent lines

Expert Solution

milcah answered 1 year ago

For the curve r=1+sin(theta), find: Location of horizontal tangent lines: Location of vertical tangent lines:

Solve the problem 43) Find equations for the horizontal and vertical tangent lines to the curve...

Solve the problem 43) Find equations for the horizontal and vertical tangent lines to the curve r = 1 - sinθ, 0 ≤ θ < 2π. Please check if your answer is correct with the following: Horizontal: y = 1/4 at (1/2, π/6), y = 1/4 at (1/2, 5π/6), y = -2 at (2, 3π/2) Vertical: x = 0 at (0, π/2), x = -3sqrt(3)/4 at (3/2, 7π/6), x = 3sqrt(3)/4 at (3/2, 11π/6)

A curve c is defined by the parametric equations x= t^2 y= t^3-4t a) The curve...

A curve c is defined by the parametric equations x= t^2 y= t^3-4t a) The curve C has 2 tangent lines at the point (6,0). Find their equations. b) Find the points on C where the tangent line is vertical and where it is horizontal.

Find parametric equations for the tangent line to the curve with the given parametric equations at...

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

Find a set of parametric equations for the tangent line to the curve of intersection of...

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 = 16 − y, (4, −1, 17)

Find a set of parametric equations for the tangent line to the curve of intersection of...

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 = sqrt(x2 + y2) , 9x − 3y + 5z = 40, (3, 4, 5)

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

3. (5 points) (a): Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.$$ x=e^{-t} \cos t, \quad y=e^{-t} \sin t, \quad z=e^{-t} ; \quad(1,0,1) $$(b): Find the unit tangent vector $\mathbf{T}$, the principal unit normal $\mathbf{N}$, and the curvature $\kappa$ for the space curve,$$ \mathbf{r}(t)=<3 3="" 4="" sin="" cos="" t="">$$

Find the point of intersection of the tangent lines to the curve r(t) = 5 sin(πt),...

Find the point of intersection of the tangent lines to the curve r(t) = 5 sin(πt), 2 sin(πt), 6 cos(πt) at the points where t = 0 and t = 0.5. (x, y, z) =

Find an equation of the tangent to the curve x = 2 + ln t, y...

Find an equation of the tangent to the curve x = 2 + ln t, y = t2 + 4 at the point (2, 5) by two methods. (a) without eliminating the parameter (b) by first eliminating the parameter

Find the distance between the skew lines with parametric equations x = 1 + t, y...

Find the distance between the skew lines with parametric equations x = 1 + t, y = 3 + 6t, z = 2t, and x = 1 + 2s, y = 6 + 15s, z = −2 + 6s. Find the equation of the line that passes through the points on the two lines where the shortest distance is measured.

Question

Find all horizontal and vertical tangent lines for the parametric curve defined by x(t) = t^3...

Solutions

Expert Solution

Related Solutions

For the curve r=1+sin(theta), find: Location of horizontal tangent lines: Location of vertical tangent lines:

Solve the problem 43) Find equations for the horizontal and vertical tangent lines to the curve...

A curve c is defined by the parametric equations x= t^2 y= t^3-4t a) The curve...

Find parametric equations for the tangent line to the curve with the given parametric equations at...

Find a set of parametric equations for the tangent line to the curve of intersection of...

Find a set of parametric equations for the tangent line to the curve of intersection of...

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

Find the point of intersection of the tangent lines to the curve r(t) = 5 sin(πt),...

Find an equation of the tangent to the curve x = 2 + ln t, y...

Find the distance between the skew lines with parametric equations x = 1 + t, y...