Question

How do you find the length of a smooth parametrized curve x = ƒ(t), y = g(t), a<= t<=b? What does smoothness have to do with length? What else do you need to know about the param-etrization in order to find the curve’s length? Give examples.

Find answers to questions asked by student like you

Q: Suppose you are looking for an item in an ordered list one million items long. How many steps might ...

A: Given,An item in an ordered list one million items longBy definition

Q: The region in the first quadrant that is bounded above by the curve y = ex - 1, below by the x-axis,...

A: Express the integral as below.

Q: what is the left and right endpoint Riemann sum for f(x)= (x^2)/11 on the interval [2,6]?

A: Given:

Q: Find parametric equations for the semicircle x2 + y2 = a2, y> 0, using as parameter the slope t =...

A: Click to see the answer

Q: find the first four nonzero terms of the Taylor se-ries generated by ƒ at x = ƒ(x) = 1/x at x =a>...

A: Given information.

Q: How would you compare the relative merits of Simpson’s Rule and the Trapezoidal Rule.

A: Compare the relative merits of Simpson’s rule and the Trapezoidal rule as given below in the Table

Q: Find the volume of the solid generated by re-volving the region in the first quadrant bounded by the...

A: First calculate the area ‘A’ under the given curve as.

Q: The ellipse (x2/16) + (y2/9) = 1 is shifted 4 units to the right and 3 units up to generate the elli...

A: First list the formulas for ellipse.

Q: Solve the exponential growth/ decay initial value problem for y as a function of t by thinking of th...

A: Given,