(1 point) Given the parametric curve *(t) =t(t? - 3), y(t) = 3(t? - 3) answer...
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) =...
0/7 points v Previous Answers V SCALCET8 10.3.062. Find the points on the given curve where the tangent line is horizontal or vertical. (Assume o ses 21. Enter your answers as a comma-separated list of ordered pairs.) r = 1 - sin(O) horizontal tangent (rio vertical tangent (r, 0) = Need Help? Read It Talk to a Tutor Submit Answer
(1 point) Consider the function f(x, y) = 4x+ + 8y. List all critical points of f(x, y). If there are none, enter "none". If there is more than one, enter a comma-separated list of ordered pairs, e.g., "(1,2), (3,4). (5,6)" Critical points are List all critical points of f(x,y) which are local maxima. If there are none, enter "none". If there is more than one, enter a comma-separated list of ordered pairs, e... "(1,2), (3,4), (5,6) Local maxima occur...
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 4 In(t), y = 6/t, z = t4; (0,6, 1) x(t), y(t), z(t) = X
Let the curve C in the (x, y)-plane be given by the parametric equations x = e + 2, y = e2-1, tER. (a) Show that the point (3,0) belongs to the curve C. To which value of the parameter t does the point (3,0) correspond? (b) Find an expression for dy (dy/dt) without eliminating the parameter t, i.e., using de = (da/dt) (c) Using your result from part (b), find the value of at the point (3,0). (d) From...
1. (3) Find parametric equations for the tangent line to the curve x(t) y(t) = 7+3 when t = 1. 5 3+212
7. (-/1 Points) DETAILS LARCALC11 11.R.037. Find sets of parametric equations and symmetric equations of the line that passes through the two points. (For the line, write the direction numbers as integers.) (7, 0,5), (10, 11, 9) (a) Find sets of parametric equations. (Enter your answer as a comma-separated list of equations in terms of x, y, z, and t.) (b) Find sets of symmetric equations. *57 - 11 3+5 0 - 7x + 3 = 11y = -5z +...
Find parametric equations for the line that is tangent to the given curve at the given parameter value. r(t) = (5+?) 1+ (2t - 1)]+(31') k, t=to = 3 What is the standard parameterization for the tangent line? X = y = ZE (Type expressions using t as the variable.)
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 >.
please answer both (12(8 pts) Find parametric equations of the line through the point (2, -1,3) and perpendicular to the line with parametric equations 1-t,y 4- 2t and 3+ t and perpendicular to the line with parametric equations 3+t,y 2-t and z 3+2t. (13)(8 pts) Find the unit tangent vector (T(t) for the vector function r(t) - costi+3t j+ 2sin 2t k at the point where t 0 (12(8 pts) Find parametric equations of the line through the point (2,...