Calculus

Can You Estimate √101 Without a Calculator?

Approximating functions with polynomials, key expansions, and convergence tests.

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What to remember

  • Taylor series approximate functions by matching derivatives at a point; low orders often suffice.
  • Memorize e^x, sin, cos, ln(1+x), (1+x)^α; they solve limits and approximations instantly.
  • Geometric series a/(1−r) prices perpetuities; ratio/root tests settle convergence.
Read the lessonTaylor Series & Sequences, with a checkpoint at the end.