Find the length of the curve r(t) = e³t cos(t), y(t) = et sin(t) for 0 < t < 10. Give an exact answer, without using a decimal. Answer entry tip: To enter e², type exp(x). To enter √, type sqrt(x).

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A: The answer is given in step 2 and 3

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A: The parametric curve has a horizontal tangent if dydt=0;dxdt≠0 and vertical tangent if dxdt=0;dydt≠0

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Q: What is the tangent line to when x = 4.2? y = x 4.7√x

A:

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A: given curve is                                                                     x=t3-3ty=t4-2…

Q: c) the equation of the tangent for y=xlnx at the point where x = e

A:

Q: Find an equation of the tangent line to the curve y=x√x that is parallel to the line y = 3 + 3x. y =

A:

Q: c) Find the equation of the tangent line to the function y = sec²x at the point (2:2).

A: Given function as y=sec2x

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A: At x=2; (2+2)2+(y+2)2=25 16+(y+2)2=25 (y+2)2=9 y+2=±3y = 1 or -5Therefore two points at which…

Q: (3x+4) cm (3x-1) cm 15 cm M NOT DRAWN TO SCALE In the diagram MN| = 15 cm. [MO= (3x- 1) cm, NO = (3x…

A:

Q: Sketch the graph of the following between x = 4T and x = 4т. y = sin x 0.5 -Зл -2л 2л 47 -0.5-

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A:

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A: