Skill — Risolvere disequazioni.
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Linked atoms
83 linked atoms.
11 Disequazioni
- A complete inequality from start to finish
- A typical literal inequality
- Case a negative, Delta negative — always negative
- Case a negative, Delta positive
- Case a positive, Delta positive
- Case Delta negative — parabola always positive
- Case Delta zero — tangent parabola
- Compact procedure for second-degree inequalities
- Constructing an inequality given the sign table
- Equivalence principles and sign reversal
- Examples of first-degree inequalities
- Factors always of the same sign
- First-degree fractional inequality
- Fractional inequality with a common denominator
- Inequality with a quadratic factor
- Simple fractional inequality
- System of two inequalities
- System with three conditions
- The sign-table method
- Third-degree inequality
12 La parabola
- Absolute value of 3x+2 less than 5 (|3x+2| < 5)
- Absolute value of x-2 less than or equal to x+1 (|x-2| ≤ x+1)
- Absolute value of x²-1 greater than or equal to 3 (|x²-1| ≥ 3)
- (x-2) ≤ 0)
- General splitting method
- Inequality with absolute values and squares (|x²-4| > |x-2|)
- Inequality with the absolute value of a trinomial (|x²-5x+6| ≥ 2x-3)
- Inequality with two absolute values by squaring (|x| < |x-1|)
- Mixed cases with two absolute values
- Special case - modulus greater than or equal to B(x)
- Special case - modulus less than or equal to B(x)
- Sum of three absolute values less than 4 (|x|+|x-1|+|x-2| < 4)
- Sum of two absolute values less than or equal to 6 (|x-1|+|x+2| ≤ 6)
13 Radicali ed equazioni irrazionali
- Inequality with the root on the greater side
- Inequality with the root on the smaller side
- Inequality with two roots
- Non-strict inequality
- Type I — root greater
- Type II — root smaller
17 Disequazioni irrazionali
- A complete example with the sign line
- A reminder about the existence conditions
- Decision map — what type of inequality am I facing?
- Example — root larger than a line
- Example — root smaller than a line
- Example — two radicals compared
- Recognising always-non-negative sums
- Squaring without splitting into cases
- The method for the larger root — Type II
- The method for the smaller root — Type I
- The sign-table strategy
- Worked exercise — Fractional inequality with a radical
- Worked exercise — Root versus absolute value
- Worked exercise — Sum of two radicals
- Worked exercise — Type I with a strict root
- Worked exercise — Type II with a semicircle
18 Fasci di rette
23 Funzioni, linguaggio e proprietà
25 Funzione esponenziale
- Exponential inequality
- Guided examples with base less than 1
- Number of half-lives
- The rule of the direction
- The trivial cases of the positive exponential
26 Funzione logaritmica
- Basic cases with base less than 1
- Logarithmic inequality with base less than 1
- Rule for the direction in inequalities
27 Metodi unificanti per equazioni e disequazioni
- A checklist for the oral exam
- Idea 1: substitution
- Idea 3: applying a monotonic function (inequalities)
- Idea 4: sign analysis
- Inequality with absolute value
- Irrational inequality
- Logarithmic inequality
32 Disequazioni goniometriche
- Absolute value of the cosine
- Elementary inequalities with sine and cosine
- Elementary inequalities with the tangent
- Elementary inequality with the sine
- Elementary inequality with the tangent
- Factorisation with the double-angle formula
- Inequalities with absolute value and roots
- Inequality reducible to the cosine
- Product of factors and sign table
- Product of factors with sign table
- The sign-study method