High number LIM (x - > 0) TaNx / x ^ 3-x ^ 2-2x why TaNx ~ x ^ 3-x ^ 2-2x ~ (- 2x)

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• 1. Find ∫ DS, where l is the circle x2 + y2 = 4
• 2. Calculate the surface integral ∫ (x ^ 2 + y ^ 2 + Z ^ 2) ^ - 0.5ds, where ∑ is the sphere x ^ 2 + y ^ 2 + Z ^ 2 = a ^ 2 (z > 0)
• 3. ∫∫ s (x + y + Z) ds, where s is the upper hemisphere, z = √ a ^ 2-x ^ 2-y ^ 2 Detailed point, this is a class of surface integral problem
• 4. Given the coordinates (1,2 times the root sign 3) of the endpoint B of the line segment AB, the endpoint a moves on the circle P (x + 1) ^ 2 + y ^ 2 = 4, find the tangent equation of the trajectory of the midpoint m in AB and P passing through point B
• 5. ∫ (X & ∫ 178; + Y & ∫ 178;) ds ∑: z = root X & ∫ + Y & ∫ 178; the part cut off by z = 2 ∫ ∫ is followed by ∑
• 6. ∫∫∑ 1 / √ (1 + 4x & # 178; + 4Y & # 178;) ds, ∑ surface z = x & # 178; + Y & # 178; (0 ≤ Z ≤ 1)
• 7. The equation for the projection of the sphere x ^ 2 + y ^ 2 + Z ^ 2 = 9 and the plane x + y = 1 on the xoy plane
• 8. The projection of the intersection line of x ^ 2 + y ^ 2 under the equation z = x ^ 2 + y ^ 2 and z = 2-radical on xoy plane,
• 9. What does DS represent in the surface integral of area in higher numbers
• 10. Let s be a sphere x ^ 2 + y ^ 2 + Z ^ 2 = 1, and find the value of surface integral ∫ (x + y + Z + 1) ds. The answer is 4 Π
• 11. High number: l is the circle x square + y square; find L (x square + y Square) ds under ∮
• 12. If you translate the straight line y = - 2x + 6 downward by how many units, you can get that there is only one intersection point between the new straight line and the hyperbola y = 1 / x?
• 13. As shown in the figure, the straight line y = 2x moves 2 units along the positive direction of x-axis, intersects with X-axis at point a, and intersects with hyperbola y = 6 / X and hyperbola y = K / X at two points BC respectively, And the area of triangle OBC = the area of triangle OAB, K=
• 14. It is known that the absolute value of x = 4, the absolute value of y = 1 / 2, and XY is less than 0, the absolute value of X of y of the ball The writing process is the best
• 15. Let l be a line segment from a (1,0) to B (- 1,2), then the curve integral ∫ L (x + y) ds
• 16. Find the curve integral ∫ L (x + y) ds, l is the straight line segment connecting (1.0) (0.1) two points. (PS: explain how DS is transformed into DX)
• 17. I = FF (x ^ 2 + y ^ 2) ds, where the surface is spherical x ^ 2 + y ^ 2 + Z ^ 2 = 2 (x + y + Z)
• 18. Let ∑ be a sphere x ^ 2 + y ^ 2 + Z ^ 2 = 4, then the curved area is divided into ∮ (x ^ 2 + y ^ 2 + Z ^ 2) ds=
• 19. The range of surface integral ∫ (a ^ 2 + x ^ 2 + y ^ 2) ^ 0.5 DS is the upper part of sphere x ^ 2 + y ^ 2 + Z ^ 2 = a ^ 2
• 20. Calculate the first curvilinear integral ∫ xyds, where C is the entire boundary of a triangle with curved edges bounded by y equal to x square, y = 0 and x = 1