Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x = cos(O) + sin(40) y = sin(0) + cos(40) O = 0 y(x) = Need Help? Read It Talk to a Tutor 2. [-14 Points] DETAILS SESSCALCET1 9.2.010. Consider the following: x = t3 - 12t y = 2 - 1 (a) Find the following. dy dr = dy dr2 = (b) For which values of t is the...
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?....
38. [-13 Points] DETAILS SCALCET8 10.2.011. Find dy/dx and dạy/dx2. x = +2 + 9, y = t2 + 5t dy dx dy ho = dx² For which values of t is the curve concave upward? (Enter your answer using interval notation.)
Find the exact length of the curve. x = 3 + 12t^2, y = 8 + 8t^3, 0 ≤ t ≤ 1
Find dy/dx and d2y/dx2 ? x = t2 + 9, y = t2 + 5t For which values of t is the curve concave upward? (Enter your answer using interval notation.)
Consider the vector field F(x, y) = (ey – ysin x + 2x, xey + cos x) (a) (4pts) Compute curl F. (b) (2pts) Is F conservative? Clearly indicate yes or no. (c) (8pts) Suppose C is the curve parameterized by r(t) = (t3 + 1, t– 2t) 0<t< 2 Compute ( F. dr.
Show work please!
The curve (x,y) = (t3 – 4t, 2t) is graphed at right. 1. (12 pts) Find the area inside the loop of the curve. Ő 2. (4 pts) Write an expression for the length of the curve in the first quadrant. (Do not evaluate.) 3. (8 pts) Find the (x,y) point in the first quadrant where the curve has a vertical tangent line.
x = t^2 - 2t + 4, y = t^3 - 6t^2
8. a) Set up the integral you would need to evaluate to find the length of the curve given in #3 if Osts 10. b) Set up the integral you would need to evaluate to find the arclength of the curve r = 4sin(30), traced out once. 3
Problem 7. Given that each of the following vector fields F is conservative Find a potential function f such that f = F and evaluate fe F dr along the given curve C 1. F(r,y) y C: F(t)(t3- 2t, t3 + 2t), 0 <t<1 2. F(x,y, ) yze"* i + e#* j + xye k C: F(t)(t2 1)i +(2 -1)( -2t)k, 0t 2
2. Consider the parametric equations x = 5 - 12, y = 13 - 481 a. Find , and determine for what values oft is the curve concave up. and when is it concave down. 2 .- der2 b. Find where is the tangent line horizontal, and where is it vertical.