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1:17Solve x² − 5x + 6 = 0 by finding two numbers with the right product and sum, then check the roots on the graph and by substitution.
1:20Solve 2x² + 3x − 2 = 0 with the quadratic formula: identify a, b and c, use the discriminant, simplify both roots and confirm them on the graph.
0:57Find the slope through (1, 2) and (3, 8), build the line y = 3x − 1 in slope-intercept form, and check both points on the graph.
0:50Differentiate 3x⁴ − 2x² + 7x term by term with the power rule, then use the derivative to find the slope of the tangent line at x = 1.
0:53Direct substitution gives 0/0 for the limit of (x² − 9)/(x − 3) as x → 3. Factor, cancel and substitute to get 6, and see the hole on the graph.
0:47Find the area under y = x² + 1 from 0 to 2 with an antiderivative and the Fundamental Theorem of Calculus: 14/3, about 4.67 square units.
0:49Differentiate (3x² + 1)⁴ with the chain rule: derivative of the outside, times derivative of the inside, giving 24x(3x² + 1)³.
0:42Use a² + b² = c² to find the hypotenuse of a right triangle with legs 6 and 8, then check the answer with the converse.
0:46With opposite side 5 and hypotenuse 13, find the adjacent side, then all three ratios: sin θ = 5/13, cos θ = 12/13 and tan θ = 5/12.
0:55Find the mean and standard deviation of 2, 4, 4, 4, 5, 5, 7, 9 step by step: mean 5, population SD 2, sample SD √(32/7) ≈ 2.14.