Michelle 發問時間： 科學數學 · 6 年前

# 大一微積分求解

1.tan(x/y)=x+y

2.if y=x^3+2x, dx/dt=5 find dy/dt when x=2

3.two radar stations at P and Q,with Q 6 km east of P, are tracking a ship which is generally to the north. at a certain instant, the ship is 5 km from P and this distance is increasing at the rate of 28km/hr. at the sme instant, the ship is also 5km from Q, but this distance is increasing at only 4 km/hr where is the ship how fast is it moving and in what direction is it moving?

4.find the greatest volume that a right circular cylinder can have if it is inscribed in a sphere of radius r.

5.suppose the wholesale price of a certain brand of medium-sized eggs p (in dollars/dozen) is related to the weekly supply x (in dozen) by the equation 625p^2-16x^2=440000 (a) if 250 dozen eggs are available at the rate of 2 dollars/dozen/week, at what rate is the supply falling? (b)if 250 dozen eggs are available at the beginning of a certain week and the supply is falling at the rate of 3 dozen/week, at what rate is the wholesale price changing?

6. if a diver of mass m stands at the end of a diving board with length L and linear density ρ, then the board takes on the shape of a curve y=f(x), where EIy'=mg(L-x)+1/2ρg(L-x)^2. E and I are positive constants that depend on the materials of the board and g is the acceleration due to gravity.find an expression for the shape of the curve.notice that the left end of the board is fixed.i.e.,y(0)=y'(0)=0

7.(a) estimate the area under the graph of f(x)=1+x^2 from x=-1 to x=2 using three rectangles and right endpoints. then improve your estimate by using six rectangles. (b) repeat part (a) using left endpoints.

8.determine a region whose area is equal to the given limit. do not evaluate the limit. lim(n->無限大) Σ(=1->n) 2/n(5+2i/n)^10

9.express the limit as a definite integral on the given interval. lim(n->無限大)Σ(i=1->n){4-3(xi)^2+6(xi)^5}△x, on [0,2]

10.express the integral ʃ(6->2) x/1+x^5 dx as a limit of riemann sums. donot evaluate the limit.

11.if f is continuous and g and h are differentiable functions, find a formula for d/dxʃ (h(x)->g(x))f(t)dt.

12.evaluate the indefinite integral ʃsinΘcosΘ (sinΘ+1)^1/2 dΘ.

13.evaluate the indicated indefinite integrals: ʃsin^10 x cosx dx.

14.find lim(n->無限大)1/nΣ(i=1->n) {(3i/n)^7+(3i/n)^4}^1/2

### 1 個解答

• 6 年前
最佳解答

(11) cont'd

f(x) ≈ 1 + π - 2x

???

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