Is the partial derivative of a function independent of the order of derivation

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• 1. There are 500 notebooks for students, 5 for each, then the function between the remaining number of books y and the number of students x is______ The value range of the independent variable x is______ ．
• 2. The unit price of a notebook is 5 yuan. It takes y yuan to buy x (x ∈ {1,2,3,4,5} laptops. Try three expressions of the function y = f (x)
• 3. If each bottle of purified water costs 2 yuan, the functional relationship between the amount of money spent on the purchase of purified water and Y (yuan) and the quantity purchased x bottles and the value range of the independent variable are given How much is it
• 4. If the derivative of F (x) = ∫ x0 (x2-t2) f ′ (T) DT is infinitesimal equivalent to X2, then f ′ (0)=______ ．
• 5. If the derivative of F (x) is infinitesimal equivalent to the derivative of G (x), then are f (x) and G (x) infinitesimal equivalent
• 6. Let f (x) have a first order continuous derivative, f (0) = 0, f ′ (0) ≠ 0, f (x) = ∫ x0 (x2 − T2) f (T) DT. When x → 0, f ′ (x) and XK are infinitesimals of the same order, and the constant k is obtained
• 7. Does infinitesimal belong to limit existence
• 8. Is the limit of infinitesimal zero?
• 9. Is it right to say that the limit of infinitesimal is 0?
• 10. Use the property of infinitesimal to calculate the following limit (1) Limx ^ 2cos1 / x where x tends to 0 (2) Lim [(arctanx) / x] where x tends to infinity
• 11. The relation between continuity and differentiability of binary function For example, if f (x, y) is continuous at point (0,0), then if x and y are all close to 0, f (XY) / (| x | y |) exists, is f (XY) differentiable at point (0,0) I know how to smoke The denominator is (| x | plus | y |)
• 12. If f (x) is a differentiable function, then dy is a linear function of △ X Why? Dy = f '(x) △ x, f (x) is a function of X, also called the linear function of △ x?
• 13. Let f (x) be differentiable, then when △ x → 0, △ y-dy is infinitesimal of higher order compared with X,
• 14. It is said that "if y = f (x) is differentiable at point x, then when △ x → 0, the differential dy of the function at point x is infinitesimal of the same order of △ X." Is this statement correct? Why? The answer is incorrect. Please explain
• 15. If y = f (x) is a differentiable function, then when △ x → 0, △ y-dy is the infinitesimal of △ X（
• 16. In a linear function y = 2x-3, if x = 0, then y = how much; when the independent variable x is, the value of the function is greater than 0 ,x=0,
• 17. Given the function y = - 2x + 3, when the independent variable x increases by 1, the function value Y () A. Increase 1b. Decrease 1C. Increase 2D. Decrease 2
• 18. For the function y equals x + 1 / X_ 1, when the value of the independent variable x is? The function value is equal to 0
• 19. What kind of function is y equal to 1 when the independent variable x is 0, and y equal to 0 when the independent variable x is finite It should be found in hyperbolic function or other trigonometric function
• 20. When the value of independent variable x satisfies what conditions, the value of function y = three-thirds of X + 6 satisfies the following conditions? （1）y=0 （2）y＜0 （3）y＞0 （4）y＜2