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기술
#### 1. Junior High Math Tools
Master foundational mathematics with intuitive, easy-to-use features:
- **Polynomial Factorization**: Instantly decompose quadratic expressions (e.g., \( x^2 - 5x + 6 \)) into factored forms (e.g., \( (x-2)(x-3) \)) to solidify algebra fundamentals.
- **Function Grapher**: Visualize linear, quadratic, trigonometric (\( \sin/\cos/\tan \)), inverse, and square root functions on a coordinate plane. Input \( y = 2x + 2 \) or \( y = \sqrt{x} \), then “Plot Function” to see curves, intercepts, and trends in real time.
#### 2. High School Science Calculators
Tackle advanced math and science concepts with targeted tools:
- **Sequence Summation**: Compute sums for *arithmetic* (using \( S_n = \frac{n}{2}[2a_1 + (n-1)d] \)), *geometric*, or *custom* sequences. See formula breakdowns (e.g., “\( S_n = 108.00 \) for \( a_1 = 3 \), \( d = 3 \), \( n = 8 \)”) to reinforce sequence logic.
- **Vector Operations**: Analyze 2D/3D vectors (e.g., \( \vec{u} = (3,4,0) \), \( \vec{v} = (1,2,3) \)) with dot products, cross products, and visualizations—perfect for physics and precalculus.
#### 3. College Engineering Mathematics
Solve complex engineering-level math with precision and depth:
- **Linear Algebra**: Manipulate square matrices to compute *determinants* (with cofactor expansion explanations), *matrix inverses* (including singularity checks for non-invertible matrices), and *eigenvalues* (with support for 2×2 and 3×3 matrices).
- **Calculus Operations**: Calculate *derivatives* (e.g., \( f'(2) = 12 \) for \( f(x) = x^3 \)) and *definite integrals* (e.g., \( \int_0^2 x^2 dx = \frac{8}{3} \)), plus view antiderivative functions (e.g., \( F(x) = \frac{1}{3}x^3 + C \)) and step-by-step reasoning.
#### 4. Experimental Data Analysis
Transform raw data into actionable insights for labs and research:
- Input experimental datasets (e.g., \( 5.2, 5.1, 5.3, \dots \)) and a reference value.
- Generate statistical results: *mean*, *standard deviation*, *relative error*, and visualize data distribution with histograms—ideal for validating experiments or analyzing trends.
With a sleek, user-friendly interface, real-time computations, and educational explanations for every result, QuantumMath is the all-in-one tool to conquer math at *any* stage—from classroom problem-solving to academic research.
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