12. Let a curve be defined parametrically by x(1) = 3cost, y(t) = 3 sint, z(1)-...
d²y Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of at this point dx x= 16 cost. y = 4 sint, t = 7 л 2 The equation represents the line tangent to the curve att (Type an exact answer, using radicals as needed.) dy The value of att is dx? (Type an exact answer, using radicals as needed.) 70 4
Question 14 5 pts Consider the parametrically defined curve a. x = 6sin(3t), y=t, z = 6cos(3t); (0,71,- 6) Find the equation of the osculating plane of the curve at the given point 4x + 18y = 18 b. X + 18y = 1871 4x - y = - 1871 d. X - 18y = - 1871 x + 18y = - 1871 C. e. a Ob С Od e
Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of at this point x=16 cost, y = 4 sint,t= The equation represents the line tangent to the curve at t= (Type an exact answer, using radicals as needed.) d²y The value of dx2 (Type an exact answer, using radicals as needed.) att =
Question 2, non-calculator Question 1, calculator The curve C in the x-y-plane is given parametrically by (x(t), y(t), where dr = t sine) and dv = cos| t The Maclaruin series for a function f is given by r" for 1 sts 6 a) Use the ratio test to find the interval of convergence of the Maclaurin series for f a) Find the slope of the line tangent to the curve C at the point where t 3. b) Let...
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...
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.
(d) Which picture shows the curve C? Recall the curve C is defined by x f(t) cost t yg(t) sint - t 2아 2아 10 10 0 0 -10 -10 -2아 -20 20 10 20 -20 10 -20 -10 0 -10 (i) (ii) X X 2아 20 1아 1아 아 0 -10 -10 -20 -2아 10 20 -20 -10 10 20 -20 -10 0 0 (iv) (iii) X X (e) Find an equation for the tangent line at the point...
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.
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 + 2 sin(t) 0<t<21 a) Express the curve with an equation that relates x and y. 7C b) Find the slope of the tangent line to the curve at the point t c) State the pair(s) (x,y) where the curve has a horizontal/vertical tangent line. 27.A particle is traveling along the path such that its position at any time t is given by r(t) =...
X) 13.4.21 Find an equation for the circle of curvature of the curve r(t)-21 + sin(t) j at the point (z,1). (The curve parameterizes the graph of y = sin | 2x | in the xy-plane.) An equation for the circle of curvature is (Type an equation. Type an exact answer, using π as needed.) X) 13.4.21 Find an equation for the circle of curvature of the curve r(t)-21 + sin(t) j at the point (z,1). (The curve parameterizes the...