conment it ASAP please
you can skip question 1 Sketch the graph of x(t) sin(2t), y(t) = (t + sin(2t))...
1. Sketch the graph of x(t) = sin(2t),y(t) = (t + sin(2t)) and find the coordinates of the points on the graph where the tangent is horizontal or vertical (please specify), then compute the second derivative and discuss the concavity of the graph 1. Sketch the graph of x(t) = sin(2t),y(t) = (t + sin(2t)) and find the coordinates of the points on the graph where the tangent is horizontal or vertical (please specify), then compute the second derivative and...
-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...
(a) Give a set of parametric equations (with domain) for the line segment from (4, -1) to (5,6). (b) Give a set of parametric equations (with domain) for the ellipse centered at (0,0) passing through the points (4,0), (-4,0), (0,3), and (0, -3), traversed once counter-clockwise. (c) Find the (x, y) coordinates of the points where the curve, defined parametrically by I= 2 cost y = sin 2t 0<t<T, has a horizontal tangent.
The velocity vector of an object is given by y(t) = (* sin(at), 1, a cos(at)). Assume that at t = 1, the object is at the point P(1,1,0). (a) Find the position vector F(t) of the object. (b) Find parametric equations of the line which is tangent to r(t) at P. (c) Find the distance that the object traveled from the point t = 0 to t = 1. (d) Find an equation for the normal plane of r(t)...
Find the area of the specified region. 15) Inside one leaf of the four-leaved rose r 7 sin 2θ 16) Shared by the circles r 3 cos 0 and r-3 sin 17) Make sure you can also convert from Cartesian coordinates to polar form and find where on parametric and polar equations there are horizontal and vertical tangent lines. Find the area of the specified region. 15) Inside one leaf of the four-leaved rose r 7 sin 2θ 16) Shared...
1a) Find dy/dx x = te', y = t + sin t b) Find dy/dx and d’y/dx2 for which t is curve concave upward x = x3 + 1, y = t - c)Find the points on the curve where the tangent is horizontal or vertical. Draw the graph x = 13 – 3t, y = t3 – 312 d) Find the area enclosed by the x-axis and the curve x = t3 + 1, y = 2t – t?....
please help! I cannot figure this out. The graph below is of the curve defined parametrically by: x-sin t and y- sin 2t -0 5 0.5 -1 (a) SET UP THE INTEGRAL TO FIND THE AREA OF THE REGION ENCLOSED BY THE CURVE AND EVALUATE (b) SET UP THE INTEGRAL TO FIND THE LENGTH OF THE CURVE TRAVERSED EXACTLY ONCE. DO NOT EVALUATE. SIMPLIFY TO JUST BEFORE MAKING A SUBSTITUION. (c) SET UP THE INTEGRAL TO FIND THE TOTAL DISTANCE...
Question 11 Find the length of the curve with parametric equations x = 2t, y = 3t, where 0 <t < 1. 10 42-2 O 4V2 - 1 22-1 4/ Question 12 True or false: y=x cos x is a solution of the differential equation y + y = -2 sin x True False
For the following equations : x= 2t^2 , y = 3t^2 , z= 4t^2 ; 1 <=t <=3 A) write the position vector and tangent vector for the curve with the parametric equations above B) Find the length function s (t) for the curve C) write the position vector as a function of s and verify by differentiation that this position vector in terms of s is a unit tangent to the curve.
Name that Parametrization 4. (a) Consider these two sets of parametric cquations: x(1)-1 y(t) = sin t 0<t<oo x (t) sin t y(t) = t 0<t<00 What is the difference between their associated curves? (b) Given any set of equations of the form What does the graph of the set of equations y(r) = 1 x(!) = f (1) 0<t<oo look like? Use a calculator to check that f(x) = x5-3x3 + 5x + 2 is one-to-one. 5, (a) (b)...