One,

1.adx=d(ax)，secxtanxdx=d(secx).

2. Let sinx be the original function of function f(x), then f(x)dx=(dsinx). Then f(x) is the derivative function of sinx.

3.fˊ(x)dx=(d f(x)), [f(x)dx]ˊ= (). (This is the first time I have seen the expression [f(x)dx])

4.(arctanx)ˇ=( 1/( 1+x？ ) )，(cscx)ˇ=(-cscxctgx).

5. Suppose when () is infinitesimal and when () is infinite. (inaccurate expression)

6. The geometric meaning of definite integral f(x)dx is (the area between curve f(x) and X axis in a given interval (between upper and lower limits))

Second,

1. The function f (x) is defined at point x0, which is the necessary and sufficient condition ((b)) that it has a limit at that point.

(a) Necessary and sufficient conditions (b) Necessary and insufficient conditions

(c) Sufficient and unnecessary conditions (d) Irrelevant conditions

2. The derivative is-Yes (none of the options is correct)

lnx (B)ln (C)ln(-x)(D)ln

3. if y = ln ~ x ~, then y = (1/x).

(A)- (B) (C)︱︱ (D)-︱︱

4. If the function is continuous at x=0, then the value of a is (). I don't know the relationship between a and x, and the relationship between a and function, so I can't answer.

1 (B) 2 (C) 3 (D) 0

5.∫e-x dx=( ex-( 1/2)x？ +C), none of the options given are correct.

(A)e-x+C(B)-e-x+C(C)-e-x(D)-ex+C

3,3 Find the concave-convex interval and inflection point of the curve y=3x4-4x3+ 1

y′= 12x 3- 12x？ ,

y ”= 36 x？ -24 x = 12 x (3 x-2), let y "= 0, and x 1=0, x2=2/3,

The curve is concave in the interval (-∞, 0), (2/3,+∞); Concave in the interval (0,2/3), there are two inflection points (0, 1) and (1, 0).

Fourth, the comprehensive question is 20 points * 1=20 points.

Write the conditions and conclusions of Rolle and Lagrange mean value theorem; (8 points)

Explain the geometric significance of the above two theorems; (6 points)

Describe the relationship between the above two theorems; (3 points)

Give examples of other mean value theorems you know. (3 points)

Baidu Library-

Rolle mean value theorem/view/de3db9ed172deD630a1cb605.html.

Lagrange mean value theorem-data collection

/view/d 78 ba 98 AEC 3a 87 c 24028 c 493 . html

Rolle-Rolle

Lagrange-Lagrange