x = 2t2 – C : 3t + 1 y = et²-1

Q: Find a function y = f(x) that describes the parametric x = -2t + 1, y = 3t², for – o <t < ∞. curve

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Q: Find an equation for the tangent plane to the surface 22 – xy? = 0 at the point (1, 3, 3).

A: Given that At point (1,3,3) Take, Now to find the divergence of f, The divergence at point…

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

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Q: Find the slope of the tangent line to the parametric equations: x = 3t2 - 3, y = 2t + 1 at t = 1. %D…

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Q: The parametric curve x= 414 + 412 + 1, y= 5t 3 – 5t has two tangent lines at the point (9, 0). Find…

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Q: Sketch the curve defined by the parametric equations x = t2, y = t + 1, -∞ &lt; t &lt; ∞.

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Q: Consider the parametric curve C: x 1+cost, y= -3+2sint, 0stS (1) Sketch the curve and indicate the…

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Q: Find the equation of the line tangent to the parametric curve (pictured below) defined by I=, y=t+t…

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Q: Sketch the curve with parametric equations x = sin t y = sin2t

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Q: Which is a parametric equation for the curve y = 9 – OA. c(t) = (t, 2 + t) OB. c(t) = (t, 9 – 2t)…

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Q: The parametric equation of a curve is given by x= cost, y= sint− cost, 0 ≤ t ≤ 1 . Without…

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Q: Consider the parametric equations x(t) = 1 + 3t2, y(t) = 4 + 21³, -1 <t <1. • What is the length of…

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Q: Given the curve with parametric equations, find the slope and the equation of the tangent line at…

A: Here we have to find the Slope of tangent line at indicated points . We are given parametric…

Q: A curve is defined by the parametric equations z (t) = e-* and y (t) = e*. What is in terms of t ? A…

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Q: Consider the parametric curve C that is defined by C: x=t^3, y=t^2+t, −1≤t≤3. (a). Find the…

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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,…

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

Q: A curve is defined by the parametric equations x (t) = at² and d² y y (t) = bt where a and b are…

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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: Find the parametric equation for the line tangent to the r(t)=sinti+(t2-cost)j+etk curve t=0 at the…

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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: 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: For which values of t is the parametric curve x=8t, y=t+t, -0c0s ts 00 concave up? (Enter your…

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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 parametric curve defined by 1 a(t) %3D y(t) = t² || What is the slope of the line…

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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: Without eliminating the parameter t, find a Cartesian equation for the lin curve C, defined by the…

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

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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: Find the exact length of the given parametric curve. X = = 8t³, y = 12t², 0 <t< 2

A: Consider the parametric equations

Q: a) Find the are length of the parametric curve x = B(t. sint), y = B(1+ cost), in the range 0 sts,…

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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(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: Eliminate the parameter to find a Cartesian equation of the curve with parametric equations x = e^t…

A: Just put the exponential term value from one equation into the other and easily eliminate the…

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

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Q: Find the equation for the line tangent to the parametric curve: t3 – 9t - 9t2 – t4 at the points…

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Q: Find an equation of the tangent line of the parametric curve, I = 1+÷, y=t³ –t² +3,

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Q: x = +4r2 +4t +1 y =1+3 at the point P(1, 1).

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Q: List all of the points (x,y) on the parametric curve x=t^3+4t,  y=6t^2 where the tangent line is…

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Q: Draw the curve given by the parametric equationsx=t3+t2−t,y=t3+2t2−4t.

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

A: Given parametric equations is x = sin t; y = 1 - cos t, 0 ≤t≤2π b) Eliminate t and determine what…

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: Find the length of the parametric curve defined by x=r°, y=t- for 0st<1 7.

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Q: Sketch the curve given by the parametric equations x= t³ - 1 and y= t² + t.

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Q: Find the length of the curve C defined parametrically by C:x(t) = e' cos t, y(t) = e' sint, 0<tS#…

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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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