Let C be the curve connecting (0,0,

Show that t, e^t, and sin(t) are linearly independent.

Let C be a piecewise curve consists of the following four line segments. First linesegment has vertices (0, 0) and (2, 0); the second segment has vertices (2, 0) and(2, 1); the third line segment has vertices (2, 1) and (0, 3); and the fourth linesegment has vertices (0, 3) and (0, 0). C is oriented counterclockwise. LetF(x, y) = ⟨x^2 − 2y, 2x⟩ be a vector field.(a) Sketch C accurately including the orientation.(b) Find the work done by F by moving a particle along the path C in the givendirection. Simplify your answer.

Find the length of the curve ƒ1x2= x3>2 between x = 0 and x = 4 (as shown).

Let C be the curve connecting (0,0) to (9,3) to (-3,3) to (0,0) using straight lines. | (sec-(æ³ + 1) – xy²)dx + (evJ+3+ 4x)dy Evaluate