Find parametric equations for the tangent line at the point (cos(−4π/6),sin(−4π/6),−4π/6) on the curve x=cos(t), y=sin(t), z=(t) x(t)= y(t)= z(t)=

Q: Eliminate the parameter to find a Cartesian equation of the curve. x=1-cos(t) y=1-sin(t)

A: We have to eliminate the parameter and find the cartesian equation.

Q: a) Plot the parametric curve x=1 – sin t, y=1+ cos t with 0 <t< ™. b) Determine the equation of the…

A: Given: For the curve x=1-sin(t) t 0 π/2 π x 1 0 1

Q: The equation of the tangent line to the parametric equations, x = sine, y= 20 + cose at 0 = 0 is y =…

A:

Q: find the parametric equations for the tangent line to the curve x=t^2-1,y=t^3+1,z=t^2 at the point…

A: Given, x=t^2-1 y=t^3+1 z=t^2 point (x1,y1,z1)= (8,28,9)

Q: I the slope of the tangent line to the parametric curve X = 3 cos (t) y = 2 sin(t) ㅠ R 4 at the…

A: Given query is to find the slope of the tangent.

Q: Consider the parametric equations x = 2t – 5, y = 6. dy Use the derivative formula from Section 10.2…

A:

Q: Find parametric equations for the tangent line to the curve with the parametric equations x…

A: Given: The parametric equations, x = t2+3,  y = ln t2+3, z = t and the point 2, ln4, 1. To find: The…

Q: 2) Graph the x, y-curve described by the parametric equation by eliminating t from the equation. x =…

A:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: given parametric equations are x=1+12t , y=t3-t , z=t3+t

Q: Find the parametric equations for the tangent line to the curve æ = t3 – 1,y = to +1, z = t° at the…

A: Find the tangent vector r't:                 r(t)=(t3-1)i +(t5+1)j +t5k Differentiate r(t):…

Q: find y'' for the curve cosx-siny=4

A:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Given:

Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint); + In…

A:

Q: Eliminate the parameter to find the cartesian equation of the curve: x = 2 sin 0, y = cos² 0, sos…

A:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A:

Q: Find the equation of the tangent line to the parametric curve x = θ+cosθ, y=1+sinθ; θ = π/6

A: We have to find equation of tangent line to the parametric curve at θ=π6 where parametric curve is:…

Q: Find the parametric equations of the tangent line LT to the curve C:r (t) = 2 cos(t)i + sin(t)j +…

A:

Q: Find the slope of the tangent to the parametric curve c(t) = (cos t, sin t) at the point (–1/2,…

A: We need to find the slope of the tangent to the parametric curve c(t)=(cos t, sin t ) at the point…

Q: Find parametric equations for the line that is tangent to the curve r(t) = e^t i + (sin t)j + ln (1…

A: The given curve is Differentiating with respect to t, we get Now, we find r(0) and r'(0) and

Q: 7. Find the first derivative of y with respect to x of the following parametric equations. x = 1 +…

A:

Q: 1. x (0) = 0 + cos 0 y (0) = 1+ sin 0 given that

A:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: The tangent line to a parametric curve given by c(t)=&lt; x(t) , y(t) , z(t) &gt; at some point…

Q: Find the exact slope of the tangent line to the parametric curve at the point where y = 2 sin(t) t =…

A: x=8 cos (t) y=2 sin (t)

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A:

Q: 9. Show that the curve with parametric equations x = sin t and y = sin(t + sin t) for 0st s 2n has…

A: Given that the curve with parametric equations are x=sint,y=sint+sint. First find the slope that is…

Q: find the equations of the tangent and normal to the curve expressed in parametric form at the point…

A:

Q: 1. Find the second derivative of the parametric equations x = a cos t and y = b sin t 2. Use second…

A:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A:

Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

A: Let r(t) be a curve, the derivative r'(t) is a vector tangent to the curve. The equation of the line…

Q: Find parametric equations for the tangent line at the point (cos(), sin(5 ), ) on the curve a = cos…

A: Here, the given parametric equation of the curver(t)=(x,y,z) where x=cos t, y=sin t, z=t. To find…

Q: Find a standard equation for the tangent plane and parametric equations of the normal line at the…

A: Introduction: If F(x,y,z) is a differentiable surface at the point (x0,y0,z0), the tangent plane to…

Q: The derivative Z of the parametric equations z= 7 sin 3t and y= cos 3t is.

A:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A:

Q: 10. Find the equations of the two tangent lines at the (-1,0) for the parametric curve x = 12- 2, y…

A:

Q: x = 2 cos(3t) – 4 sin( 3t) IT t = 2 y = 3 tan( 6t)

A: given,        x=2cos3t-4sin3t   and y =3tan6t

Q: 3. Find the equation of the tangent line to the curve C given by the parametric equations x= e', y=…

A:

Q: Find an equation of the tangent(s) to the curve with parametric equations x = 1 + √t, y = e^(t^2)…

A: Given parametric equation of curve x=1+t   y=et2we want to find equation of tangent at  ( 2, e)

Q: B) Find parametric equations for the line that is tangent to the curve r(t) = e'i + (sin t)j + In(1…

A:

Q: Consider the parametric curve x = sint + cos t, = cos² t 0 <t < 2n п Find an equation for the…

A: We find dx/dt and dy/dt from the given equations

Q: Sketch the curve by using the parametric equation to plot points. Then, eliminate the parameter 0,…

A:

Q: {; 4 cos(t) 2 sin(t) at the point 4 Find the slope of the tangent line to the parametric curve

A: We have the parametric equation of curve as x=4cost⇒cost=x4        ⋯⋯1y=2sint⇒sint=y2          ⋯⋯2…

Q: Find the second derivative of y with respect to x from the parametric equations given. x = 3 + 4…

A:

Q: 1 cos(t) ly = 3 sin(t) Find the slope of the tangent line to the parametric curve at the point

A:

Q: Find the parametric equations for the tangent line to the curve x=t^4−1, y=t^3+1, z=t^2 at the point…

A: Consider the given curves and points.

Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x2 +?…

A: Given      x2 + z2 = 25 and y2 + z2 = 25 at the point (3,-3,4) Let    f(x,y,z) = x2 + z2 - 25  and…

Q: 2. Find the parametric equations for the line tangent to the curve given by r(t) = cos ti + sin tj +…

A:

Q: r(t) = (e-t cos t, e-t sin t, e-t)

A: Given  rt=e-tcost,e-tsint,e-t First find derivative of given point dxdt=-e-tcost-e-tsint…

Q: The velocity of a particle moving in the xy plane is given by the parametric equations dx/dt=…

A: The given parametric equations of the particle is dxdt=-2t sin2t and dydt=2t cos2t. Evaluate the…

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.