질문 calculus1 듣는데요!! 제발~~!!! 한국인 위상이 달려있어요 ㅜㅜ

[나두몰러~]

여기는 미국인데요

대학교를 다니고있는데 칼큘러스를 듣고있어여

교수가 한국사람들은 수학 딥따 잘한다고 칭찬해줘서 한참 기가 살아

있었는데 집에서 풀으라고 내준 수학문제를 도저히 못풀겠어요

이대로 못풀어가면 체면이 말이 아닐텐데 제발 도와주세요!!

4. lim ( cos x - cos 3)/(x-3)
x=>3

gives the slope of the graph of a function at a point. What function at what point?

A. f(x) = sin x, at x = sin 3
B. f(x) = cos x, at x = sin 3
C. f(x) = sin x, at x = 3
D. f(x) = cos x at x = 3
E. none of these

8. If f(x) = sec (ln x), then f '(x) =

A. cos (ln x)
B. -(1/x)[sin (ln x)]
C. [sec (ln x)]2
D. -(1/x)[csc (ln x)]2
E. sin (ln x)
F. (1/x)[cos (ln x)]
G. -[csc (ln x)]2
H. (1/x)[sec (ln x)]2
I. none of these

11. The upper end of a straight ladder is leaning against the vertical side of a building, with its lower end on a horizontal sidewalk. To the consternation of the painter standing on it, the upper end is slipping down the wall at a constant rate of 2 feet/sec. The lower end is, therefore, sliding along the sidewalk. Having had a course in the Calculus, the painter is, of course, interested in how fast the lower end is moving. If the ladder is 17 feet long, how fast is the lower end moving when the upper end is 15 feet above the ground?
A. 8/3 feet/sec.
B. 3/2 feet/sec
C. 48/7 feet/sec.
D. 7/12 feet/sec.
E. 15/4 feet/sec.
F. 16/15 feet/sec.
G. none of these


12. If f(t) represents the distance, in meters, of an object from some fixed location (the origin, for our purposes) at time t, in seconds, along a straight line (the x-axis, for our purposes) and f(t) = 2t2 - t + 4, then the average velocity between t = 2 sec. and t = 4 sec. would be, in meters per second,
A. 11
B. 15/14
C. 17
D. 19/18
E. 5/4
F. none of these


13. The number of tons of garbage, G(t), to be disposed of at the end of t years from now for a certain Metropolis is G(t) = 106(2t + 1)2. How many more tons of garbage will have to be disposed of at the end of four years than at the end of three years?
A. 13,000,000
B. 32,000,000
C. 15,000,000
D. 24,000,000
E. none of these
22. t(x) = ln (cos e^2x ). Then t'(x) =
A. 2e2x cot e2x
B. 2e2x tan e2x
C. 2e2x (sec e2x )(csc e2x )
D. -2e2x (sec e2x )(csc e2x )
E. -2e2x cot e2x
F. -2e2x tan e2x
G. none of these


23. An object moves along a horizontal line under these conditions: its position with respect to a reference origin is given by s(t) = -24t^3 + 72t - 5, where positive is to the right, s is in meters, t is in seconds, and t> 0 . Then which of the following statements is true?
A. Its acceleration is always negative.
B. Its velocity is always negative.
C. Its position at t = 3 is to the right of its position at t = 0.
D. Its position is never at s = 0.
E. All of the above are false.

25. A hotel manager has 200 rooms available for rent each night. Experience shows that if she charges $45 per night, she will have full occupancy, but that for each $5 that she increases the price, 4 rooms become vacant. All other factors being equal, what will her maximum revenue be? (Points: 4)
A. $16,820
B. $13,520
C. $8820
D. $12,000
E. $11,520
F. $18,000
G. none of these


여기다 올려도 되는건지 모르겠는데 만약 아니라면 딴 게시판으로

옮기께요!!

어쨋뜬!!!! 수학전공자님들 부탁드려요~~~ 영어라 죄송~

[Fermat, Pierre de]

우헷... 영어다..-_-;; (8)번 과 (22)번은 그냥 초월함수 미분 같은데.. 캘큘러스 같은 책을 자세히 본 적은 없지만... 초월함수와 합성함수 미분에 대한 내용 나와있을껄요?

[where is..]

이런거 다 책에 나오지 않나요. 영어가 안되시는건가.-_-

[^EINSTEIN^]

그냥 definition만 이용해서 대입만 하시면 되는데여...

[Fermat, Pierre de]

문제들을 쭉 보니까.. 주로 변화율에 대한 문제군요....식만 잘 세운다면...-_-;;

[G/Z(G)]

일본어를 조금 배운 다음에 일본인인 척 하세요^^

[Fermat, Pierre de]

제가 고등학교 에서 배울때는 미분에서 변화율과 관련한 문제들로 한꺼번에 배웠답니다. 원하신다면 다 해석해서 풀어드리죠..ㅋㅋㅋ