(a) Sketch the curves: i. z (t) = t² + 2t +i (t+1), -1

Q: Find the point where the tangent line to the curve 7(?) = (V? +3,ln(?² +3),t) at (2, In 4,1) 5. %3D…

A:

Q: x(t)=2t? \yle)=r²–4¢ a) For -5sts5 , find all points (x, y) where the slope of this curve is zero.…

A: Part (a):   The slope of the parametric curve x = x(t) , y = y(t) represent the rate change dy/dx at…

Q: Consider the following. C: line segment from (0, 0) to (2, 4) (a) Find a parametrization of the path…

A: Given- C: line segment from (0, 0) to (2, 4)

Q: 8. For the curve given by r(t)=√√² +8 i + In(t² + 8)j + tk 2 find: a. r'(t)

A: Introduction: For a vector curve rt=ati+btj+ctk, the tangent line at the point of contact t=t0 is…

Q: Please do 4

A: 4. (a) To Evaluate: ∫C​x ds, where C is the arc of the parabola y=x2 from (0,0) to (1,1). Let x=t,…

Q: At which point does the parametric curve given by x = 2 cost y = 2 sin t z = 2t - π/3 cross the…

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Q: 4. First, sketch a picture of the line which passes through P = (1, 1, 2) that is perpendicular to…

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Q: ind the equation of the plane tagent to the curves f (t) = [3t+4,4 tº, sin (πt) + 4] and g(s) = [8°…

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Q: 3. Let f(x, y) = xy+ y². Find the equation of the tangent line in parametric form in the x-direction…

A: Solve the following

Q: Consider the set C = {(x, y) E R | x-xy 2). (a) Show that C is a curve. (b) Find a parametrisation…

A: Solution (a): Given Set C=x,y∈ℝ2| x2-xy=2 Curve: A curve is continuous and smooth flowing line…

Q: Investigate the direction of convexity of the curve defined by the parametric…

A: To Determine: The direction of convexity of parametric curves x(t)=a(t-sint) , y(t)=a(1-cost) ,…

Q: The curve graphed below has the parametrization C = {(v 4 %3|

A: Introduction: A parametric equation is one in which the dependent variables are defined as…

Q: 3. Given F(x,y)=(y,2x), find F-T ds where curve C is the parabola y=x from point (0,0) to point…

A: We use line integration to evaluate this.

Q: Write the following curve in a parametric way z(t)=x(t)+iy(t) for z*z conjugate+i(z-zconjugate)-2=0

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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: 3. Consider the curve defined by the parametrization r(t) = (t cost, tsint, 232t³/2), t € [0,67],…

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

Q: i y-jx x* + y* Q.5 (a) Compute |F.dr, where F and c is the circle x + y = 1 Use parametric equations…

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Q: The helix r,(t)= (1+cost,- sint,t) intersects the curve (2,0,0). Find the angle of intersection. i,…

A: Given,           Both intersects each other at the point (2, 0, 0). We have to find the angle of…

Q: Find the length of the parametric curve x = 1+ 15t², y = 4+10t³, 0≤t≤ 1.

A: We have to find the length of the given parametric curves

Q: Consider the paraboloid given by the equation: z = x^2 + y^2 Find the equation of the tangent…

A: at point (1, 2, 5)at point (1, 2, 5)

Q: Write a parametrization for the straight line path from the point (3,3, 4) to the point (5, 2,-4).…

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Q: Find T, N, and k for the space curve r(t) = (7e'cos t)i + (7e'sin t)j + 4k.

A: Given data:  r(t)=(7et cost) i +(7et sin t) j+4k

Q: 61. (a) Show that dB/ds is perpendicular to B. (b) Show that dB/ds is perpendicular to T. (c) Deduce…

A: Introduction: The dot product, also known as the scalar product or inner product, is an algebraic…