5

True or false: Determine if the following statements are true orfalse. Briefly justify your answers. Simply writing “true” or“false” will ea...

Question

True or false: Determine if the following statements are true orfalse. Briefly justify your answers. Simply writing “true” or“false” will earn you zero credit. (a) If C is any differentiablecurve starting at the origin and ending at (2, 1), then Z C 2xydx +x 2 dy = 4. (b) It is possible to find a differentiable curve Cstarting at a fixed point A and ending at a fixed point B so that ZC y 2 dx = 5 and Z C y 2 ds = 3.

True or false: Determine if the following statements are true or false. Briefly justify your answers. Simply writing “true” or “false” will earn you zero credit. (a) If C is any differentiable curve starting at the origin and ending at (2, 1), then Z C 2xydx + x 2 dy = 4. (b) It is possible to find a differentiable curve C starting at a fixed point A and ending at a fixed point B so that Z C y 2 dx = 5 and Z C y 2 ds = 3.



Answers

$$
\begin{array}{l}{\text { True or False If a function } y=f(x) \text { is differentiable on an }} \\ {\text { interval }[a, b], \text { then the length of its curve is given by }} \\ {\int_{a}^{b} \sqrt{1+\left(\frac{d y}{d x}\right)^{2}} d x . \text { Justify your answer. }}\end{array}
$$

So for this problem, does it make sense that if X cubed is a factor of a differentiable function? So let's say it's X cubed times glX. So that means X cubed is a factor because it's just multiplying by some other stuff. So if X cubed is a factor then what's the derivative? And can I divide out an X squared? So basically is why prime divisible by X. Where? So let's find why prime using the product rule that would be three X squared times G plus the derivative of G, prime times X. Cute. So is this divisible by X squared? Well, if you factor out an X squared, you're left with three times G plus X times G. Prime. So yes, X squared is a factor of why prime? This is true.

So in this question we have to give an excellent explanation for the statements whether it is true or false. The statement is the girl which is given paramedic lee By the equation x equals two ft and bicycles. The duty has no sharp corners. If the function F and G are defensible like so the statement is true and we'll talk about the explanation for this statement. So in this we learn about the concept of parametric equations, right? So the apologies. Let's assume a contradiction to the police statement. Let's say we have a sharp corner on the graph of why it was his ex. So in that case the um I D X will not be defined late. Mhm. But we also know that day by by the X. Can be with Dennis, divide by DT divided by DX by DT. Which means that since developed by the X is not defined. Which means that either divide by DT all the X by D day is not defined. It means that either the function affects or the function G. X. It's not defensible right? Which is false under the assumption that is a function F energy being differential, being differentiated. Therefore, the statement is true. Okay?

We're going to solve a problem about 14 here. The U. N statement is took since radiant, radiant, off function F is normal. But a goat is normal. Don't seat. Thank you.

So the demand for this one will be forms. And we can take one context and go here so we can have from my and be here and we can had a function dot Ah, it will be different people and increasing on the time. But it will have the inflection poem on this phone saying, and it's gone here. Maybe the onesie here and I just born here. The Brown did say he could do zero because it is an impression point and ah, that's why in the estimate his phones


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