iven the parametric curve x = 3t² – 1, y = 2t3 + 1. (a) Find the equation of the tangent to the curve that passes through the point (2,3) (in point-slope form). (b) Find the area under the curve for te [0, 2]. (c) Find the length of the curve for t e [0, 4].

Q: 5. The curve C has parametric equations = (In t)? – Int, y = In t2 - t2, (1) Find the exact…

A:

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

A:

Q: x(t) = 3 cos t y(t) = 8 sin t 0<t< 2n a) What does the curve described by these parametric equations…

A:

Q: 4. Sketch the graph of the curve y = Vx and the tangent line in the Cartesian Plane using a scale of…

A:

Q: For the cycloid described by the parametric equations x = 2(t - sint) and y = 2(1- cost), a) find…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Parametric equations of a curve are given as 4 and y=t+- 2 x = 2t d’y when t = -4. where t + 0.…

A:

Q: The plane y = 1 intersects the surface z = x° + 5xy – y* in a certain curve. Find the slope of the…

A:

Q: e Green's Theorem to evaluate [(-y²)dx + (x²)dy if the curve C is a triangle with rtices at (0,0),…

A: Top:- application of integration

Q: #3. Find parametric equations for the tangent line to thể curve with parametric equations x = (sin…

A:

Q: Consider the curve given by the parametric equations: (x = 3t² - 6t ly = t4 2t³ - 2t² - 2t +6 a.…

A: It is provided that the parametric equation of the curve is: x(t)=3t2-6t, y(t)=t4-2t3-2t2-2t+6. We…

Q: x(t) y(t) = 3 sin t 8 cos t 0<t< 2n a) What does the curve described by these parametric equations…

A: Recall: Equation of line: y-y1=mx-x1 ; where m=dydx or  y2-y1x2-x1 Length of the curve…

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

A: Given:

Q: (a) Find the slope of the tangent line to the parametric curve x = 3cos t, y = 4sin t at t =…

A: Given, x=3cost,y=4sint at t=π4 and t=7π4. Differentiate the functions x and y with respect to t.…

Q: 39 A parametric curve is given by x =1- y=1+ 0. dy in term of t and evaluate it at 1=-2. dx a. Find…

A:

Q: a) Find the equation of tangent line of curve that is given by parametric equations X = 3cost + sint…

A: (a) Given  parametric form of curve is…

Q: The diagram shows the curve with parametric equations y= 2 sin'r+ 3 cos'r +1 x= 2- cos 21, for 0 <rs…

A:

Q: i) Find g1 (0, 5). ii) Find g2 (0, 5). iii) Find the equation of the tangent plane to the surface z…

A: First option is correct

Q: Tangent are drown from the origin to the curve y = sin x.Prove that their points of contact lies on…

A: Consider the curve y=sinx Here, the objective is to prove that the point of contact of tangent from…

Q: 2. Find the length of the curve 1<t<4. given by r= e'(sin t+cos t), y = e'(cos t-sin t), OS

A:

Q: Find parametric equations for the tangent line at the point (cos(), sin(²), ) on the curve x = cos…

A: Given query is to find the parametric equation of the tangent.

Q: Let C₁ be the curve with parametric equations I= cost, y = sint -t, where t € [0, 1]. (a) Find the…

A:

Q: 5. For the Parametric curve x = a(t – sint), y = a(1 – cost) where 'a' is a constant. Find y d?y at…

A:

Q: 1. Given: parametric curve H defined by r(t) = tan-¹ t and y(t) = e¹, where t € R (a) Find the slope…

A: Solved below.

Q: The plane y 1 intersects the surface z = x' + 5xy – y in a certain curve. Find the slope of the…

A: To find the slope of the tangent line of the curve: z=x7+5xy-y4 And the plane y=1, at the point…

Q: Find the momen

A: Given: r2=a2sin2θ

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

A:

Q: The differential of plane curves described. 1. the cissoids y^2 = x^3 / (a-x)

A: y^2 = x^3 / (a-x)

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

A: Here, the given parametric equation of the curve is: r(t)=(x(t),y(t),z(t)) where x=6et, y=t e2t, z=t…

Q: Use the theorem to find the slope of the line x = 4t, y = 2t, for - ∞ &lt; t &lt; ∞.

A: According to the theorem, the slope is given by - dydx = dydtdxdt…

Q: The parametric equation of the tangent line to the curve C defined by the following parametric…

A: given: the parametric equation of the curve C is given by: where . we have to find the parametric…

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

A:

Q: The tangent line to a smooth curve r(t)=f(t)i+g(t)j+h(t)k at t=t0 is the line that passes through…

A: The curve is r(t)= (sin t)i + (cos t)j + (sin 2t)k, t0= π2. Obtain the point: rπ2= (sin π2)i + (cos…

Q: Find an equation of the plane tangent to the following surface at the given point. V3 cos (xyz) =…

A:

Q: x = 2 cos(t) Find the slope of the tangent line to the parametric curve at the point y = 3 sin(t)…

A: The derivative dydx defines the slope of the tangent drawn to the curve.

Q: 1. Given the parametric curve x = 3t2 – 1, y = 2t³ + 1. (a) Find the equation of the tangent to the…

A: Please refer the attached image for complete solution.

Q: A cycloid has parametric equations z =t - sint, y = 1 - cost, 0 <t< 2x. Find the slope of the…

A:

Q: 1 A curve C is defined by the parametric equations x = and y = for 1z 0. VI +1 t + 1 dy (a) Find dx…

A: First find slopes then us equation of tangent line

Q: A SPACESHIP IS TRAVEIING WITH ACCELERATION act) = , AND HAD INITIAL VELOCITY v (0) = <1,0,0). FI ND…

A: A spaceship is traveling with acceleration a(t)=&lt;et,t,sin2t&gt; At t=0,…

Q: curve has a parametric equation x = and y = t. Find t-3 dy when t =1. dx d'y dx?

A: Given that, the parametric equations are x=tt-3 and y=t2. Differentiate the x=tt-3 with respect to t…

Q: n equation of the plane tangent to the following surface at s(xyz) = 1,1, (z.1 is ation of the…

A:

Q: x=e-t Cost y=e-t S int  find the equations of the tangent and normal lines of the parametric curve…

A:

Q: Find the arc length of the curve y = e® from x=0 to x=1. VIte-1 VIte+1 - (v2 + ¿ln a. V2+1 Ob.…

A: Consider the equation: y=ex……1 from the limit x=0 to x=1.

Q: Find equation of (a) the tangent plane to the given surface at the specified point. y = e^x cos (z)…

A:

Q: Slope of the Curve r = f(0) in the Cartesian xy-Plane dy dx f'(0) sin 0 + f(0) cos e f'(0) cos 0-…

A: When we describe a curve using polar coordinates, it is a curve in the xy-plane.  We able to compute…

Q: Pis the curve given by parametric equations x=1. y=r,z=, 1s152 x =t, y =r, z =r, 1st52 Calculate the…

A:

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

A: We find parametric equations for the tangent line to the curve with the given parametric equations…

Q: 13. Consider the curve C given by the parametric equations x=2–3cos t and y = 3+2 sin t, for –sis 2…

A: Formula a) dy/dx b) y-y1 = (dy/dx)(x-x1)