Find a parametrization for the curve. The upper half of the parabola x−1 = y2 Choose the correct answer below. A. x =t2+1 , y =t,t≥0B. x =t, y =t2−1 ,t≥0C. x =t, y =t2+1 ,t≤1D. x =t2−1 , y =t,t≥1E. x =t, y =t2−1 ,t≥1F. x =t2+1 , y =t,t≤0
Find a parametrization for the curve. The upper half of the parabola x + 10 = y 2 Choose the correct answer below. A. x = t , y = t 2 + 10 , t ≥ 0 B. x = t 2 − 10 , y = t , t ≥ 0 C. x = t , y = t 2 + 10 , t ≥ 10 D. x = t 2 − 10 , y = t , t ≤ 0 E. x = t , y = t 2 − 10 , t ≤ 10 F. x = t 2 + 10 , y = t , t ≥ 10
Use the ratio test to determine whether ∑ n = 19 ∞ 2 n ( 7 n ) 2 converges or diverges. (a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n ≥ 19 , lim n → ∞ | a n + 1 a n | = lim n → ∞ (b) Evaluate the limit in the previous part. Enter ∞ as infinity and − ∞ as -infinity. If the limit does not exist, enter DNE. lim n → ∞ | a n + 1 a n | = ◻ (c) By the ratio test, does the series converge, diverge, or is the test inconclusive? Choose