Five knowledge points in the second chapter of senior three mathematics (1)
1. The general solution of the function domain: 1, and the denominator of the fraction is not equal to zero;
2. The number of even roots is greater than or equal to zero;
3. The real number of logarithm is greater than zero;
4. The bases of exponential function and logarithmic function are greater than zero and not equal to1;
5. Trigonometric tangent function y = x ≠ kπ+π/2InY = tanx;
6. If the function is an analytical formula determined by the actual meaning, its value range should be determined according to the actual meaning of the independent variable.
Second, resolution function's common solution:
1, define the method;
2. Alternative methods;
3. undetermined coefficient method;
4. Function equation method;
5. Parameter method;
6. Matching method
Three, the common solution of function range:
1, substitution method;
2. Matching method;
3. Discrimination method;
4. Geometric method;
5. Inequality method;
6. Monotonicity method;
7. Direct instruction
Four, the common methods to find the maximum value of the function:
1, matching method;
2. Alternative methods;
3. Inequality method;
4. Geometric method;
5. Monotonicity method
Five, the common conclusion of monotonicity of function:
1. If both F (x) and G (x) are increasing (decreasing) functions in an interval, then f(x)+g(x) is also increasing (decreasing) function in this interval.
2. If f(x) is an increase (decrease) function, then -f(x) is an increase (decrease) function.
3. If the monotonicity of f(x) and g(x) is the same, then f[g(x)] is increasing function; If the monotonicity of f(x) and g(x) is different, then f[g(x)] is a decreasing function.
4. Odd functions have the same monotonicity in symmetric intervals, while even functions have the opposite monotonicity in symmetric intervals.
5. Monotonicity solution of common functions: size comparison, domain evaluation, maximum value, inequality solution, inequality proof and function image making.
Six, the common conclusion of function parity:
1. If a odd function is defined at x=0, then f(0)=0. If a function y=f(x) is both a odd function and an even function, then f(x)=0 (otherwise it will not hold).
2. The sum (difference) of two odd (even) functions is an odd (even) function; The product (quotient) of is an even function.
3. The product (quotient) of odd function and even function is odd function.
4. A function consisting of two functions y=f(u) and u=g(x). As long as one of them is an even function, then the composite function is an even function; When both functions are odd function, the composite function is odd function.
5. If the domain of the function f(x) is symmetrical about the origin, then f(x) can be expressed as f (x) =1/2 [f (x)+f (-x)]+1/2 [f (x)+f (-x)].
Three mathematics in the second chapter compulsory five knowledge points (2)
One deduction deduces the sum of the first n terms of geometric series by dislocation subtraction: sn = a1+a1q+a1q 2+…+a1,
Use q: qsn = a1q+a1q 2+a1q 3+…+a1qn,
Subtract the two expressions to get (1-q) sn = a1-a1qn, ∴Sn=(q≠ 1).
Two preventive measures
(1) From an+ 1=qan, q≠0, we can't immediately assert that {an} is a geometric series, so we should verify a 1≠0.
(2) When using the first n terms and formulas of geometric series, we must pay attention to the classification and discussion of q= 1 and q≠ 1 to prevent mistakes caused by ignoring the special situation of q= 1.
Three methods
The judgment methods of geometric series are as follows:
(1) Definition: If an+ 1/an=q(q is a non-zero constant) or an/an- 1=q(q is a non-zero constant and n≥2 and n∈N*), {an} is a geometric series.
(2) Term formula: In the sequence {an}, an≠0 and a = an an+2 (n ∈ n *), then the sequence {an} is a geometric series.
(3) General formula method: If the general formula of series can be written as an = cqn (both c and q are constants not equal to 0, n∈N*), then {an} is a geometric series.
Note: The first two methods can also be used to prove that a series is a geometric series.