Cxy? ds, where is the closed curve shown in the following figure:(2.3)(4.3)(5,1)...

Find $\int_{C} x d s,$ where $C$ is the curve $x=5 y^{3}$ joining (0,0) to (5,1).

So for this problem, which is have to find the smoke at point t this my brother, because we had already have a straight line. So because sloping point days going to be the soap all along this curve and so it's just a change of wire with change of ex seleka is still my intercepted X enters up truths 90 for the X intercept and 0 18 for the Y intercept. So that's going to be changing. Y is going to be Ciro 18 divided by nine minus zero. So that's going to give us a so at point a negative, too.

Question here. Rather ask us to graph out why is equal to X to the power of 3/5. So what is this going to look like? It's gonna have some sort of curve like that. Where are vertical tangent is, for sure going to occur at the, um, origin in this part particular case. So for part B here, it asks us to confirm this with our limit calculations. So we know that as X here can exhibit all real numbers where it can go between plus and minus infinity. In this particular case, we know that this is going to have to occur at the origin through which we can see graphically here.

Here wants us toe graph the curve of why is equal to X the power 5/3 minus five times X to the power of to over three. So if we graph it out on our grid, it's gonna look something like this where we're gonna have a, um, sharp incline and then a wrapping around like that. So from here, there is going to be no vertical, um, tangents. This is because at a point of a tangent, where is where we get to symmetric um, lines. However, there is no symmetry in this particular line. So from here, it wants us to verify using previous techniques sought in exercises 35 36. So in this particular case, as there is no value of X that we can isolate, there is going to be no limit. So limit is not found here. And therefore because of that, the tangent does not exist.

Alright, problem 38. Just looking at this graph. It looks like we have attention to Mexico. Zero. Okay, so let's verify this in part B. So using the definition slow, take the limit from the left. Ah h to the 3/5. When is they're over? Age C equals infinity. Take the limit. His age approaches zero from the right of H 3/5. When zero over age, it's also you're going to infinity. So the limit is each approaches zero goes to infinity, meaning we have a vertical attention at X equals zero.