Let C be the parametric curve defined by                         x(t) = t2 - 2;                         y(t) = t3 - 3t + 1: Determine if C is concave up or concave down at (-1,3):

Q: 21 Let F(x, y) = (3x + 2y)i + (2x - y)j. Evaluate F. dr where C is the curve X y from (0, 0) to (1,…

A: Here we calculate the integral along the curve x = y2 from (0,0) to (1,1)

Q: Find parametric equations for the tangent line of the curve r(t) = (3+ 3/7, to – 5t2 + 4, 3t³ + 2t²…

A: Find the parametric equations fot the tangent line

Q: - Use the graphs of = irection in which the curve is traced as t increases. = f(t) and y = g(t) to…

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Q: Let C be the closed curve indicated in the diagram. Use Green's Theorem (2,1) (o,i) (x² + y?, y³ +…

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Q: Which of the following is dy for the curve dx defined by x° – y³ = 2xy? 3x2-2y а. 2x+3y2 3x2-2y b.…

A: Find the derivative of the given curve and match with the correct option.

Q: 13. Find an equation for the tangent plane of the graph of f at the point (xo, yo, f(xo, yo)) for:…

A: Note:-Since you asked multiple questions which are not interlinked to each other, according to our…

Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

A: given ∫C2y+4zdx+2x+3zdy+4x+3ydz where C is the curve given by rt=t3,2sinπt2,3cosπt2 for 0≤t≤1…

Q: The length of a curve given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in the…

A: Given information: Parametric equation of curve is : x=x(t)y=y(t)z=z(t) We need to find the length…

Q: Q2: Evaluate . f ds where C is the given oriented curve r(t) = (-2 + 6t ,5 + 8t) for (0 <t< 1) and…

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Q: 2. Find thé moving trihedral of the curve C traced by the vector-valued function R(t) 4 cost i+4…

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Q: Let C be the parametric curve defined by æ(t) = t? – 2, | y(t) = t3 – 3t + 1. Determine if C is…

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Q: Compute f ds for the curve specified. f(x, y) = V1 + 9xy, y = x3 for 0 < x < 2.

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Q: Let F(t) = Find a parametric equation of the line tangent to r(t) at the point (157, 16, 4.159)…

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Q: Let C be the curve consisting of line segments from (0, 0) to (1, 1) to (0, 1) and back to (0, 0).…

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Q: Let y : IR → R be the parametric curve Y(t) = (, t, t). Find the coordinates of a point P on this…

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Q: Find the length of the parametric curve: x = 2t + 1; y = t? – 3,0 <t < 5

A: Given that: x=2t+1,  y=t2-3,0≤t≤5To  calculate   dxdt  and   dydt,dxdt=ddt2t+1=2dydt=ddtt2-3=2t

Q: 10. Find the value of 2 for the parametric curve xx= y = 2t2 -6 at the point (1.-6).

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Q: 13. If F-xyi-y² j, evaluate [F-dr where C is the curve y=2x² in the xy-plane from (0,0) to (1,2).…

A: The given problem is to evaluate the line integral of the given vector field over the path C curve…

Q: Let C be the parametric curve defined by x(t) = t² – 2, y(t) = t³ – 3t + 1. Determine if C is…

A: Given that,A parametric curve C is defined byx(t)=t2-2y(t)=t3-3t+1The concavity of the parametric…

Q: The parametric curve 7(t) = t2 i + (3 – t) j + et k as: 2t – 1+ e = 0 - = ť², y = 3 – t, z = et t? +…

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Q: Let (t)=(-5t2+4,t³-+4,2+³) 7 Find the line (L) tangent to (t) at the point (-1,0,2) L: (x,y,₁2)= +t

A: The given problem is to find the line tangent to the given parametric curve at the given point…

Q: Find the length of the curve r(t) (1,t²,), 0sts1 %3D «3 Ost<1

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Q: Let C be the curve in the x-y plane defined by the equation (x – h) + v – k)* =? where h, k, and r…

A: Equation of the curve is x-h2+y-k2=r2 &amp; a, b is a point on the given curve. a). Slope of the…

Q: Let C be a plane curve given by the parametric equations x = f(t), y = g(t), a ≤t≤b. Suppose that C…

A: Let a curve C be parametrized by x= f(t) and y = g(t),

Q: . Evaluate SF.dr: ▪ F = (x+z)i +zj+yk. C is the line from (2,4,4) to (1,5,2).

A: Since all subparts are different and not interlinked so as per our guideline we are supposed to…

Q: Evaluate § F · ds, where F = 2x(x+y)i + (x² + xy + y?)j and the positively-oriented curve C encloses…

A: Here we will use greens theorem to find line integral of vector field For a vector field F→= Pi^+Qj^…