Find the value of the expression.ln e5
A. 5
B.
C. 1
D. e ln 5
Answer: A
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Provide an appropriate response.Which of the following space regions is (are) closed?i.The hemispherical region centered at the origin with z > 0 and radius r bounded by 0 ? r ? roii.The xy-planeiii.The half-space x > 0iv.Space itself
A. ii, iii, and iv B. iv only C. ii only D. ii and iv
Evaluate the line integral along the curve C.ds , C is the path from (1, 1, 0) to (e4, e4, 1) given by:C1: r(t) = e4ti + e4tj, 0 ? t ? 1C2: r(t) = e4i + e4j + 10tk, 0 ? t ? 1
A. (e12 - 1) + e8 +
e4
B. (e12 - 1) + 10e8 + 50e4
C. (e12 - 1) + 10e8 + 100e4
D. (e12 - 1)
Use mathematical induction to prove the following.1 ? 3 + 2 ? 4 + 3 ? 5 + . . . + n(n + 2) =
What will be an ideal response?
Use a combination of rules for exponents to simplify. Write answers with only positive exponents. Assume that all variables represent nonzero real numbers.
A. 622 B. 67 C. 618 D. 611