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The second question:

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This part of the extended materials mainly examines the knowledge points of calculus:

A branch of mathematics that studies the differential and integral of functions and related concepts and their applications in higher mathematics. It is a basic subject of mathematics, including limit, differential calculus, integral calculus and its application. Differential calculus, including the calculation of derivatives, is a set of theories about the rate of change.

It makes the function, velocity, acceleration and curve slope can be discussed with a set of universal symbols. Integral calculus, including the calculation of integral, provides a set of general methods for defining and calculating area and volume.

Let Δ x be the increment of point m on the curve on the abscissa y = f(x), Δ y be the increment of the curve on point m corresponding to Δ x on the ordinate, and dy be the increment of the tangent of the curve on point m corresponding to Δ x on the ordinate. When | Δ x | is very small, |Δy-dy | is much smaller than |δx | (high-order infinitesimal), so we can use a tangent line segment to approximate the curve segment near point M.

If the increment of a function can be expressed as Δ y = a Δ x+o (Δ x) (where a is a constant independent of Δ x) and o (Δ x) is infinitely less than Δ x, the function f o(δx) is said to be at one point.

Is differentiable, a Δ x is called the differential of the function corresponding to the increment of the independent variable Δ x at point x0, and it is denoted as dy, that is, dy = a Δ x. ..

Usually, the increment Δ x of the independent variable X is called the differential of the independent variable, which is denoted as dx, that is, dx = Δ x. Then the differential of the function y = f(x) can be written as dy = f'(x)dx. The quotient of the differential of the function and the differential of the independent variable is equal to the derivative of the function.