[10] 9. Use a graphing calculator to sketch the graph (on this paper) of the parametric curve 24t, y2 - 4t. Estimate the coordinates of the point where the graph crosses itself. Confirm your estimate...
(1 point) A parametric curve r(t) crosses itself if there exist t s such that r(t)-r(s). The angle of intersection is the (acute) angle between the tangent vectors r() and r'(s). The parametric curver (2 -2t 3,3 cos(at), t3 - 121) crosses itself at one and only one point. The point is (r, y, z)-5 3 16 Let 0 be the acute angle between the two tangent lines to the curve at the crossing point. Then cos(0.997 (1 point) A...
The parametric curve r=(2t2+8t−5,−2cos(πt),t3−28t)r=(2t2+8t−5,−2cos(πt),t3−28t) crosses itself at one and only one point. The point is (x,y,z)=(x,y,z)= ( , , ). Let θθ be the acute angle between the two tangent lines to the curve at the crossing point. Then cos(θ)=cos(θ)= (1 point) The parametric curve r (2128t 5,-2 cos(t), 281) crosses itself at one and only one point. The point is (x.y,z- Let 0 be the acute angle between the two tangent lines to the curve at the crossing point....
please explain how you do part (b) clearly. Given the curve x-t5, y--t+4t +3, find the exact values: 18) a) of the coordinates of the leftmost point on the curve. (Use Calculus and show your work). b) of the parameter t where the graph crosses itself. (Use any method you wish - but show your work). c) of the parameter t where the slope of tangent line to the curve is(Use Calculus and show your work).
BREAKING NEWS Eyeballing Ellipses Evidence that Implicit Differentiation Works The graph of x2 -xy y2 = 4 is a tilted ellipse, as shown below. Sketch the approximate tangent lines on the ellipse where the slopes of the tangent lines are (a) zero and (b) undefined by "eyeballing". Label the coordinates with your best estimate to two decimal places. Then, use implicit differentiation to determine the exact values of the coordinates. Express your answers as proper square root ratios. Use a...
9. Here is a graph of the relation xy - y2 = 6. a) Confirm that the point (5,2) is in the relation. 5 [2 pts] -5 0 5 > -5 b) Find the slope of the tangent line through (5,2) Use methods of Calculus - do not just estimate. [ 5 pts)
1. Sketch the curve given by the parametric equations: (please use dashed lines on graph f or t beyond ) by eliminating the parameter ?. Label the direction a point on the curve moves as ? increases. PLEASE GIVE FULL WORKING FOR THE QUESTION. We were unable to transcribe this image4
Use a graph to estimate the coordinates of the rightmost point on the curve x = 2t – 4to, y = et Then use calculus to find the exact coordinates. (x, y) = (1
The parametric equations where 0 tl describe the line segment that joins the points P1(x1, y and P2(x2, y2) Use a graphing device to draw the triangle with vertices A(1, 1), B(3, 4), C(1,7). Find the parametrization, including endpoints, and sketch to check. (Enter your answers as a comma- separated list of equations. Let x and y be in terms of t.) A to B B to C A to C The parametric equations where 0 tl describe the line...
just make circle questions which 2,(b) and 3,(i) thank you 2. (Polar Coordinates: Polar Plots). (a) Consider the curve given in polar coordinates (i) Use a scientific calculator to fill in the following table with the (approximations of) values of the function r(0) on π, π r(e) (the approximations of the values r(e) must be good to at least two decimal places). (i) Use the graph paper for the polar coordinate system (attached to the assignment sheet) to plot the...
question 12 , please sketch it by your hand , do not use computer graph θ varies from 0 to 2 π. φ varies from 0 to π/4 while 0 is constant. find 9-10 Write the equation in spherical coordinates. 9. (a) :2-x2 + y2 10. (a) a-2r+y- (b) x2 +z2 = 9 (b) x + 2y+ 3:-1 11-14 Sketch the solid described by the given inequalities. 15. A solid lies above the cone:- + y and below the sphere...