At time t, the position of an ant moving in the xy-plane is given by parametric functions (x(t),y(t)), where dx/dt = 3^t +2 and dy/dt =t^2 − 4. At t=1, the position of the ant is at (2,3). a. Is the curve representing the path of the ant concave up or down at t=6? Justify your answer. b. Find the y coordinate of the ant at t=4

Q: ay or dx. 2x + y = 7x - 6 to find y a)

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: differenetiate parametrically to find dy/dx in terms of t:  x=1/t+1 , y=2t^2-4

A: please use according to form i did solved two equation because your question is not write clear that…

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A: We will use parameterization to find line integral

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Q: 1) Find the linearization L(x) of f(x) at x = a. f(x) = 2x2 + 4x - 1, a =

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the tangential and normal components.  r(t)=(t+1)i+2tj+t^ 2 × k     ,   t = 1

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: dz where C denotes a 22 Contour C=2e' with a deleted onigin. (2#0)

A: For the solution of the problem follow the next step.

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A: We can use concept of critical points in order to solve the given problem.

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Q: d/dx (2x'y²+8x-2y+3)=? Select one: a. xºy2 b. 14x°y? O c. 14x®y²+8 С. d. 14x°y²+2y O e. 2x'y?+8x-2y

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A: Slope of a curve: For non- linear functions, the rate of change varies along the given curve. So,…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.