- Inverse exp(y)−4; input domain x>−4; t=ln(5)/2.
- Factor (x−4)(x+4); limit 8. The original is undefined at 4, so not continuous there.
- exp(−x)(2x−x²), using product and chain; 2x/(2+x²), using chain. Both domains are all real x.
- Critical x=5; endpoint comparison gives minimum 10. On [6,10] the function is increasing, so minimum at 6 with value 61/6.
- Antiderivative x³+x gives 10; fundamental theorem plus chain gives 3exp(3x).
- Substitution gives e−1; parts gives 1−2/e.
- Integral 8c=1 so c=1/8; mean 8/3; probability 1/4. Density is zero outside support.
- First equals 1 by a limit; second diverges as ln T. Finite cutoffs always give finite numbers for both.
- At most 2(0.2)³/6 = 0.0026667. This is an upper bound, not the measured error.
- n²≥1/0.0006, so n≥41. After k halvings midpoint error ≤2/2^(k+1); k=10 suffices. State continuity and reliable signs for the root result.