Find parametric equations for the tangent line to the curve with the parametric equations x =sqrt(t^2 + 3), y = ln(t^2 + 3), z = t at the point (2, ln4, 1). show all steps

Q: 6. Use parametric differentiation to find if x= 212 +2, y=t* -7 dx Solution:

A:

Q: Find the length of one arc of the curve whose parametric equation are x=2θ-2sinθ and y=2-2cosθ.

A: We have to find length of arc whose parametric equations are : x=2θ-2sinθ and y=2-2cosθ Suppose 0 ≤…

Q: Find the point-slope equation of the tangent line to the parametric curve given by x = 1+ 2t° and y…

A:

Q: Find the equation of a curve passing thorugh the point (0,2) and having slope x +ex-sinhx at any…

A:

Q: Find all equations of the tangent line to the common curve of the two surfaces with equations z = x²…

A: follow next step

Q: Use first principle rule and prove that dy if y= secl tann = secx

A: To Prove: That the derivative of y=sec x is dydx=sec x·tan x. Concept used: First principle: The…

Q: x=e"Cost = e"S int

A: Given: x=e-tcosty=e-tsint At t=0: x=1, y=0 Differentiating both with respect to t:…

Q: 2. Find the equation of the tangent plane to the surface z = 3++ at point (-4, 3).

A: Topic- application of derivatives  Tangent to surface

Q: Find the equation of the tangent plane to the surface y = 2x2 - z2 at the point (0, –1, –1) %3D | |

A:

Q: Tangent drawn from the point (4, –3,10) to the intersection curve of z = x² and z = 25 – y² surfaces…

A:

Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: (a) How do you find the slope of a tangent to a parametric curve?

A: (a) Assume a general parametric curve. Differentiate and find the derivatives.

Q: 5) Find the equation of the tangent plane to the surface exyz= x + 2y + 3z at the point (3,-1,0).

A: Find tangent plane to the surface

Q: Find a parametrization of the curve. The vertical line passing through the point (3, 2, 0)

A: Consider the given point  3 , 2 , 0

Q: Find parametric equations for the normal line to the surfacez=ln(3x2 +7y2 +1)  at the point…

A:

Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 − 4z2 = 21,    (−3,…

A:

Q: Find the slope of the tangent line to polar curve r=9sinθ at the point (9/√2,π/4)

A:

Q: Find an arc-length parametrization of the line passing through (1, 0, 1) and (1, 2, 3). Upload an…

A:

Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x = 74…

A: given curves x2+z2=74 , y2+z2=74 , point 5,-5,7  to find parametric equations for the tangent line…

Q: What is the equation of the tangent line to the function y = e-* - arcsin) x+1 2. at x= 0 ? A) y-…

A:

Q: The projectile is thrown at the angle of 45 degrees with the initial velocity of 1 meter per second.…

A:

Q: Find the second derivative of y with respect to x from the parametric equation given; x =…

A:

Q: 12. Find an equation for the tangent plane to the surface given by 2xy = 2z2 - ryz at the point…

A: Use tangent plane formula

Q: What is the slope of the tangent line to a curve with parametric equations of x= 2t+1 and y= 3t-1? *

A:

Q: Find the tangent plane to the surface 8x2+y2+4z2 = 25 at the point ( 1, -1, 2 )

A: To find: The equation of the tangent plane at the point  1,-1,2. The given function for the surface…

Q: The curve with parametric equationsx = (1 + 2 sin θ) cos θ, y = (1 + 2 sin θ) sin θis called a…

A:

Q: Find the tangent plane to surface 8x2 + y2 + 4z2 = 25  at the point ( 1, -1, 2 )

A:

Q: Find the equation of the osculating plane of the helix x = sin 2t, y = t, z = cos 2t at the point…

A: The helix is given as x=sin 2t, y=t, z=cos 2t. We have to find the equation of the osculating plane…

Q: How do I find the bounds in which I integrate a curve that is rotated about an axis?

A: To find the bounds, it is necessary to check whether we have to find the surface area or volume. In…

Q: parametrik equaton of Hhe Jine thfeugh and Find Use Y For the parameter

A: Parametric equation of a line passing through a point P and parallel to a vector v is  u→(r)=P+r.v→…

Q: Find the slope of the tangent line to polar curve r=5sinθ at the point (5/2,π/6).

A: This question is related to Straight line, we will solve it using given information.

Q: Find the parametric equations of the tangent line to the curve of intersection of the surfaces x² -…

A: The equation of the tangent plane to the surface f(x, y, z)=0 at x0, y0, z0 is defined as: fxx0, y0,…

Q: 4. Find an equation for the tangent plane to the surface z = 3x + 5y + arctan in the point (0, 1,…

A:

Q: Find the tangent line to the curve 2y + " = ye"-2 at the point (2, ). %3D Please select file(s)…

A:

Q: parametrically

A:

Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 − 7z2 = 27,   (−3,…

A: Differential equations are those equations of mathematics that involve dependent variables ,…

Q: 2dy -2y 2. zt at

A: Solved below

Q: the max and min directional derivative and their directions; (4) the parametric equation of the…

A:

Q: A particle moves along the parabola y = x2 in the first quadrant in such a way that its x-coordinate…

A: It is given that the x coordinate increases at a steady 10 m/sec. dxdt=10msec. The equation of…

Q: Find the equation of the tangent plane to the graph of f(x, y) = In (13x² 10y²) %3D at the point (1,…

A: Solution is written in below steps.

Q: Find an equation of the tangent plane to the given surface at the specified point. 5Vy Z = (-1, 1,…

A:

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

A:

Q: Find an equation of the tangent plane to the surface at the given point. x² + y2 – 5z2 = 140, (-8,…

A: We will solve the problem

Q: Compute the equation of the tangent plane to the surface: y = 1 - x2 - 2z2 At the point (0, 1, 0)

A:

Q: Find the second derivative of y with respect to x from the parametric equations given.

A: The objective is to Find the second derivative of y with respect to x from the parametric equations…

Q: nit vector that is parallel to the

A: Here have to find the unit vector that is parallel to the line tangent to the parabola y = x2 at the…