2. For x>-1. the sequence defined recursively by x1 = 2"+1| ¹ [√₁+2x₂ −1].20 converges to In(x, +1). Arrange this formula in a way that avoids loss of significance.

Alice has asked you to help her classify these functions based on their asymptotic growth rate. That is, she wants you to prove a tight big-Theta bound for each function by following these steps. i. Use algebra to simply the function for ease of analysis. Remember the goal of simplification is to isolate terms and identify the dominant term. For instance, we might want to expand (n + 1)² to n² +2n+1 to see that n² is the dominant term. ii. Use your intuition, the limit test, or algebra to come up with a good guess of a tight bound. For instance, after isolating n² as the dominant term we might guess our polynomial is in (n²). iii. Use the limit test or the definitions to prove that your guess is correct. Both methods can provide correct proofs, and its a good idea to practice both methods. Sometimes our guess is incorrect and we need to return to the previous step. Transcribed Image Text: Alice has asked you to help her classify these functions based on their asymptotic growth rate.…

Without computing any Fourier series, address the following statements regarding the functions below:

The DNA molecule comes in the form of a double helix, meaning two helices that wrap around one another. Suppose a single one of the helices has a radius of 6 A (1 angstrom = 10-8 cm) and one full turn of the helix has a height of 31 A. Find the paremetrization r(t) of the helix. r(t) = (6 cos(1), a, b) (Use symbolic notation and fractions where needed.) a = b = Find the arc length L of one full turn of the helix. L=

Need ans for part a only