distinguish
Derivative is an important concept in calculus, which indicates the rate of change of a function at a certain point. The operation steps of derivation are as follows:
1. First, express the function as an expression about the independent variable x.
2. Then, find the derivative of the function, that is, find the derivative of the function at a certain point.
3. The formula is: f' (x) = lim (h->; 0)[f(x+h)-f(x)]/h, where h is the limit.
4. Pay attention to the continuity and differentiability of the function when taking the derivative. If the function is discontinuous or nondifferentiable at a certain point, then the derivative at that point does not exist.
comprehensive
Integral is another important concept in calculus, which represents the area or volume of a function in a certain interval. The operation steps of integral are as follows:
1. First, express the function as an expression about the independent variable x.
2. Then, determine the upper and lower limits of the integral and the integral form, which can be definite integral or indefinite integral.
3. The formula of definite integral is: ∫ [a, b] f (x) dx = lim (n->; ∞) σ [f (xi) δ x], where δ x = (b-a)/n, and n is the divisor.
4. The formula of indefinite integral is: ∫f(x)dx=f(x)+C, where c is constant and F(x) is the original function of F(x).
limit
Limit is another basic concept in calculus, which indicates the trend of a function at a certain point. The operation steps of the limit are as follows:
1. First, determine the limit value of the function at a certain point.
2. Then, use the definition formula of limit to calculate, namely lim (x->; a)f(x)=L .
3. The calculation of limit needs to pay attention to the continuity and differentiability of the function at this point. If the function is discontinuous or differentiable at this point, then the limit does not exist.
final result
Calculus is an important subject in higher mathematics, involving basic concepts such as derivative, integral and limit. In practical application, calculus can be used to solve many problems, such as finding the slope of the curve, finding the area under the curve, finding the volume and so on. By mastering the basic formula of calculus, we can better understand and apply the knowledge of calculus.