Find the length of the curve defined by the parametric equations y3In(t/4)2-1) from t 5 tot- 7 ...
The region inside the curve r= 4 cos θ and outside the curve r = 2. r(t) 2 rt)4cos(t) -1 What are the coordinates of the point where the two circles intersect at the top of the picture in terms of (r,0) What are the coordinates of the same point in cartesians coordinates (x.y)? Give an equivalent version of the point in polar coordinates with r <o. What is the slope of of the tangent line to the circler 2...
QUESTION 2 Let C be the curve represented by the parametric equation x(t) = ? +61 +12t+36 yt=+1 Find an equation for the tangent line at the point t-1 on the curve C. Where on the curve is the tangent line vertical? Attach File Browse My Computer QUESTION 3 Express the Cartesian coordinates (-1,1) in polar coordinates in at least two different ways. Attach File Browse My Computer
Question 15 < > Find the length of the curve for the following parametric equations for 2 <t < 10. Find its exact value, no decimals. r(t) = e' - 36 ly(t) = 2461/2 Length =
2t from Find the length of the parametric curve given by r(t) = 2 – logt and y(t) t=l to t= e.
1. a. Consider the curve defined by the following parametric equations: r(t) = et-e-t, y(t) = et + e-t where t can be any number. Determine where the particle describing the curve is when tIn(3) In(2). 0, ln(2) and In(3). Split up the work among your group Onex, vou l'ave found i lose live polnia, try to n"惱; wbai ille wlu le curve "u"ht lex k like. b. Verify that every point on the curve from the previous problem solves...
(1 point) Find the length of the curve defined by the parametric equations 3 -1, X = y = 3 ln((t/4)2 – 1) from t = 6 to t = 7.
3. (5 points) (a): Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=etcost, yr etsint, z=et; (1,0,1) (b): Find the unit tangent vector T, the principal unit normal N, and the curvature k for the space curve, r(t) =< 3 sint, 3 cost, 4t >.
-1-1 arctan n n" n!5* (c) Find the interval of convergence and radius of convergence for )0301 i )e-3r) (d) Use the geometric series to write the power series expansion for i. f(1)- 2-4r, centered at a = 0. i.)4 centered at a-6. (e) Write the first 4 nonzero terms of the Maclaurin expansion for i, f(z) = z2 (e4-1) ii. /(x) = cos(3r)-2 sin(2x). (0) Use the Taylor Series definition to write the expansion for f(a)entered at (8) Use...
Need help with both 4 and 5 4. ㅢ5 points SCalcET8 10.PP.501.XP. A curve is defined by the parametric equations below. Find the length of the arc of the curve from the origin to the nearest point where there is a vertical tangent line. Need Help? Talk to a Tter Read It Submit Answer Save Progress . 15 points SCalcET8 11.PP.006 Find the sum of the series 2 3 4 6 8 9 12 where the terms are the reciprocals...
Please help me on the following homework problems, thank you! 1. Let C be the parametric curve given by (x(t), y(t)), whose graphs are shown below. Both consis t entirely of quarter-circles and line segments. The domain of this curve is [0,10] x(t) y(t) 4 4 0 1 2 3 4 5 6 7 89 10 t 0 1 2 3 4 5 6 789 10 t (a) Find the area of the region in the xy plane bounded by...