a) Since
we get
b) Since
this arc-length parameter is
c) Let us write ; we have
Thus,
and since
we see that, with new parametrization, becomes the circle .
Consider the parametric curve F(t) = (2+1 - 2)i+2 4 13 (a) (10 points) Evaluate SF(t)dt....
3. (12 points) Consider the curve C defined by r(t) = (4 sint, -4 cost,0) with t € (0,2) (a) Compute the length of the curve C. (b) Parametrize f(t) with respect to arc length measured from t=0. (c) Determine the curvature of C.
Consider the parametric curve given by x(t) = 16 sin3(t), y(t) = 13 cos(t) − 5 cos(2t) − 2 cos(3t) − cos(4t), where t denotes an angle between 0 and 2π. (a) Sketch a graph of this parametric curve. (b) Write an integral representing the arc length of this curve. (c) Using Riemann sums and n = 8, estimate the arc length of this curve. (d) Write an expression for the exact area of the region enclosed by this curve.
Consider the parametric curve given by x(t) = t^2 − 2, y(t) = 2t^3 + 3, What is the length of the arc from the point (−1, 1) to the point (2, −13)
4.Consider the curve described by the parametric equations x= sin(t)=cos2(t) ,y= sec(t). Verify that all points on this curve satisfy the equation x^2+y^2=y^4
8.) (13 pts.) Assume that curve C is given parametrically by F(t) = ($(t)) i + (g(t)) ; + (h(t)) k for t20. Let s = s(t) be the arc length of curve C from t = 0 to t. Assume that the unit tangent vector is given by 1 S T(t) = T(t(s)) = + V5+ sa 5 + s2 Find the curvature of C when the arc length is s = 2. v6+ 2 75 5 + 32
Select the first set of parametric equations, x = a cos(bt), y = c sin(dt). (a) Set the equations to x = 2 cos(t), y = 2 sin(t) using the sliders for a, b, c, and d. Describe the parametric curve. This answer has not been graded yet. What minimum parameter domain is required to draw the entire circle? Osts How many times is the circle traced out for Osts 4? Click the Animate button and observe the relationship between...
Question 6 14 pts Consider the curve C defined by the parametric equations: x f(t) y= g(t) = sint -t costt (d) Which picture shows the curve C? Recall the curve C is defined by : x= f(t) cos t g(t) = sint - t y 20 20 10 10F 0 -10 -10 -20 -20 -20 10 -20 10 C 20 -10 0 10 (i) (ii) X 20 20 10 10 0 0 10 -10 -20 -20h -20 10 -20...
need help Find the length of the curve defined by the parametric equations y3In(t/4)2-1) from t 5 tot- 7 Find the length of parametized curve given by a(t) -0t3 -3t2 + 6t, y(t)1t3 +3t2+ 0t, where t goes from zero to one. Hint: The speed is a quadratic polynomial with integer coefficients. A curve with polar equation 14 7sin θ + 50 cos θ represents a line. Write this line in the given Cartesian form Note: Your answer should be...
3. (12 points) Consider the curve C defined by r(t) = (4 sint, -4 cost,0) with t€ (0,2) (a) Compute the length of the curve C. (b) Parametrize fit) with respect to are length measured from t = 0. (c) Determine the curvature of C.
Consider the parametric equations below. x = 2 + 4t y = 1-t2 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.(b) Eliminate the parameter to find a Cartesian equation of the curve. y = _______ Consider the parametric equations below. x = 3t - 5 y = 2t + 4 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the...