Worked Math Solutions
Explore worked examples in calculus, algebra, geometry, and statistics. Each solution shows the method, the calculation, and a way to check or interpret the answer.
Calculus
Find the derivative of sin(x)
Use the limit definition and the angle addition identity to show why the derivative of sin(x) is cos(x).
Read the solution →Calculus
Integrate ln(x) dx
Evaluate the integral of ln(x) by choosing u = ln(x) in integration by parts.
Read the solution →Algebra
Proof of the quadratic formula
Derive the quadratic formula from ax² + bx + c = 0 by completing the square.
Read the solution →Geometry
Calculate the area of a circle with radius 7
Apply A = πr² to a circle with radius 7 and find both the exact and approximate area.
Read the solution →Calculus
Find the Maclaurin series for e^x
Build the Maclaurin series for e^x from its derivatives and show the first several terms.
Read the solution →Statistics
Calculate sample standard deviation
Find the sample standard deviation of eight values by computing the mean, squared deviations, and sample variance.
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