Find the length of arc of the curve given by the parametric equations x = t°, y=t² from the point (-1, 1) to the point (8,4).

Q: A curve is defined by the parametric equations x = sint, y = 1– cos t, 0 <t< 27.

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Q: Find the parametric equations of normal line to the surface given by f(x,y) = tan Vx2 + y² at the…

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Q: Sketch the plane curve represented by the given parametric equations x = 4 cos t + 2, y = 4cos t -…

A: We first make a table for the function t 0 π/2 π 3π/2 2π x 6 2 -2 2 6 y 3 -1 -5 -1 3

Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

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Q: Eliminate the parameter t from the parametric equations x = 3 cos t, y = 5 sin t and then sketch the…

A: In eliminating parameter t from the given parametric equations we do establish the relationship…

Q: Evaluate the arc length of the curve generated by the parametric equations below for t (-1,1) x(t)=…

A: The expression for the arc length of the parametric curve is; L=∫abx't2+y't2dt   Given: xt=3+3t2 ;…

Q: Find the equation of the plane perpendicular to the curve r(t) = (sin(2t), t, cos(2t)) at the point…

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Q: Find the equation of the tangent plane at the point (1, 2, 7) to the surface given by x³ sin(z) +…

A: Consider a surface F(x,y,z)=0. Then the equation of the tangent plane to the surface F at the point…

Q: Find the radius of curvature at 0 = t of the parametric equations x = 3(0 + cos 0), y = 3(1 – cos…

A: To find the radius of curvature, first find out dxdθ and d2xdθ2. x=3θ+cos θdxdθ=31-sin θd2xdθ2=-3cos…

Q: Find a parametrization for the curve y = Vx with terminal point (0, 0) using the angle 0 in the…

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Q: x = 2t2 – C : 3t + 1 y = et²-1

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Q: Find an equation of the tangent plane to the given parametric surface at the specified point x = u?,…

A: x=u2 y=vu2 z=uv u=3 v=4 x1 =u2   x1 =9 y1 =vu2   y1=36 z1=uv z1 =12 we have to find the tangent…

Q: Find the length of the curve defined by the parametric equations 3 -t, y = 3 In((t/4)? – 1) x = 4…

A: Given:- x =(3t/4)  y = 3ln((t/4)2-1)  To find:- Length of curve from t =5 to t=6

Q: Eliminate the parameter t from the parametric equationsx = 3+1 2 sec t and y =2+  4 tan t.

A: Given parametric equations are x=3+12 sect and y=2+4 tant We have to eliminate the parameter t from…

Q: Consider the parametric curve given by x = t2 + 5, y= e* est + 2t. 3t Find the slope of the tangent…

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Q: Sketch the curve defined by the parametric equations x = sin πt/2, y = t, 0≤ t ≤ 6.

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Q: Eliminate the parameter in the parametric equations x = 7+ sint, y = 2+ sint, for 0sts, and describe…

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Q: Find the slope of the tangent to the parametric curve c(t) = (cos t, sin t) at the point (-1/2,-V3).

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Q: A curve is defined by the parametric equations sin z dz, CoS Z dz, t 2 1. y= X= Find the length of…

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Q: Find parametric equations for the tangent line to the curve a-tcost, y-t, z- tsint at the

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Q: Find the tangent line(s) to the parametric curve given by a = t-9t and y =t at (0, 9) %3D %3D

A: We have to find the tangent line

Q: Sketch the parametric curve at R* whose parameterization is given by a (t) = (cos (t), sin (1), t),…

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Q: Consider the curve given by the parametric equations x = sin t, y = sin(t + sint) where -oo <t < ∞.…

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Q: Compute the length of the curve given parametrically by x=1/3t^3 and y=1/2t^2 for 0 less or equal to…

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Q: Find the exact value of x²y³z ds, where C is the curve with parametric equations x = e-t cos(5t), y…

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Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

A: Let's find.

Q: Find the parametric equations for the tangent line to the curve x =t* _ 1,y=t* +1,z=t* - at the…

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Q: Which type of surface does the curvex= cos(3t),y= sin(3t),z=t, lie on?

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Q: A parametric curve is defined by : I) x = 5sin(t ) – 2; y = 1– 3 cos(t ) ; 0sisa

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Given the parametric curve. x = cos t y = sin t 0 <t< 2T Please find the length of curve.

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Q: Find an equation of the tangent(s) to the curve with parametric equations x = t cost, y = tsin t…

A: Given- x=tcost , y=tsint To find - To find the equation of tangent to the curve with given…

Q: CHOOSE ONE. Find the length of the curve x = 4- y (a) using the parametric equations r = 2 cos t and…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Find the arc length of the curve on the given interval. Parametric Equations x = 5t + 5, y = 7- 2t…

A: The parametric equations of the given curves are   x=5t+5,  y=7-2t and the given interval is -1≤t≤3…

Q: Find the parametric equations of normal line to the surface given by f(x, y) = tan v x2 +y2 at the…

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Q: Find the length of the curve having a parametric equation of x= 2cos³0 and y=2sin²0 from 0-0 to…

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Q: Sketch the plane curve represented by the parametric equations x = 6 cos t, y = 4 sin t, π ≤ t ≤ 2π…

A: Given  x = 6 cos t, y = 4 sin t, π ≤ t ≤ 2π

Q: Find the length of the parametric curve x = 2t + 1, y = 3 + 2tž, 0 < t <%.

A: Find the Length of the curve

Q: Find an equation of the tangent plane to the parametric surface x=5rcosθ, y=4rsinθ z=r at the point…

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Q: Find the equation of the tangent plane at the point (-2,1 – 3) to the ellipsoid surface + y? + = 3.

A: Find the equations of the tangent plane and normal line at the point (-2, 1, -3) to the ellipsoid…

Q: Find parametric equations for the semicircle x2 + y2 = a2, y&gt; 0, using as parameter the slope t =…

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Q: Find an equation for the tangent plane to the surface z +4 = ry" cos(2) at the point (4, 1, 0).

A: Use the partial differentiation for finding the tangent plane.

Q: What is the equation for the line tangent to the parametric curve I = 4 sin(2t) y = 4 sin(t) at t=…

A: Explanation: Given that: x=4sin2ty=4sintt=π6or 30° Concept used: The standard equation of line…

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: Find T(t) and a set of parametric equations for the tangent line to the helix given by 7(t) = 2…

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Q: 2. Find an equation of the tangent plane to the parametric surface F(u, v) = (, 2uv, uv?) at the…

A: (2) Consider the provided question,

Q: What is the equation of the plane that is tangent to the graph of z = x coS y – ye“, when (x, y) =…

A: Equation of the plane tangent to the surface z=f(x,y) :               Let   F(x,y,z) =0 ,then…

Q: Sketch the plane curve represented by the parametric equations x = 5 cos t, y = 2 sin t, 0 ≤ t ≤ π…

A: x=5cost,  y=2sint Now,…

Q: Find the distance between the point (4, −1, 5) and the line given by the set of parametric equations…

A: The point is: P(4, −1, 5) The line is: x = 3, y = 1 + 3t, z = 1 + t The line is: &lt;3, 1, 1&gt; +…

Q: Consider the parametric curve C defined by x = x (t) and %3D y = y (t). (a) How do you find the…

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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.