A) x0 = 0 B) x0 > 0 C) x0 < 0 D) x0 >= S
A) S != 1 B) S = 0 C) S < 0 D) S > 0
A) x_n <= 0 B) x_n = 0 C) x_n < 0 D) x_n > 0
A) (sqrt(S) / x_n) - 1 B) x_n / S - 1 C) S / x_n - 1 D) (x_n / sqrt(S)) - 1
A) epsilon_n < -1 B) epsilon_n <= 0 C) epsilon_n >= 0 D) epsilon_n > -1
A) S / (1 + epsilon_n) B) S * (1 + epsilon_n) C) sqrt(S) * (1 + epsilon_n) D) sqrt(S) * epsilon_n
A) epsilon_n2 / (1 + epsilon_n) B) 2 * epsilon_n2 / (1 + epsilon_n) C) epsilon_n / (2(1 + epsilon_n)) D) epsilon_n2 / (2(1 + epsilon_n))
A) epsilon_{n+1} = -1 B) epsilon_{n+1} >= 0 C) epsilon_{n+1} <= -1 D) epsilon_{n+1} < 0
A) min { epsilon_n2 / 2, epsilon_n / 2 } B) min { epsilon_{n+1}2 / 2, epsilon_{n+1} / 2 } C) min { epsilon_{n+1}2, epsilon_{n+1} } D) min { epsilon_{n+1} / 2, epsilon_{n+1}2 / 4 }
A) Quadratic B) Cubic C) Linear D) Logarithmic
A) The cube root B) The negative square root C) The non-negative square root D) The reciprocal
A) Integers B) Rational C) Irrational D) Prime numbers
A) To some finite precision B) To infinite precision C) Using exact fractions D) By guessing the exact value
A) A random sequence of numbers B) A single exact formula C) A geometric progression of errors D) A series of increasingly accurate approximations
A) They are always exact B) They are iterative C) They are non-computable D) They are linear
A) Calculating the final error B) Squaring the number S C) Dividing by zero D) Choosing a suitable initial estimate
A) A Taylor series is integrated B) An iterative refinement is performed C) The number S is discarded D) The algorithm terminates immediately
A) When the computer crashes B) When the estimate becomes zero C) Until some termination criterion is met D) After exactly two steps
A) Taylor's method B) Babylonian division C) Newton's method D) Euclid's method
A) If division is much more costly than multiplication B) If infinite precision is required C) If S is a negative number D) If division is faster than multiplication
A) Using prime factorization B) Using Taylor series C) Using geometric proofs D) Using logarithmic addition
A) Binomial expansions B) Continued fraction expansions C) Decimal expansions D) Fourier series expansions
A) The programming language syntax exclusively B) Only the color of the output screen C) Needed accuracy, available tools, and computational power D) The user's age and location
A) Mental calculation, paper and pencil, and digital computers B) Ancient, medieval, and futuristic C) Fast, slow, and impossible D) Integer, fraction, and decimal
A) The speed of the computer processor B) How many iterations are required to achieve a specified precision C) The total memory used by the program D) The size of the input number S
A) Error propagation B) Initial estimation C) Termination criterion D) Computational complexity
A) All iterative methods B) Babylonian approximation methods C) Heron's method and Newton's method D) Paper-and-pencil synthetic division and series expansion
A) The exact square root of a prime number B) A square root calculated without decimals C) The square root rounded or truncated to the nearest integer D) The square root multiplied by an integer
A) Since the 20th century CE B) Since the Renaissance in Western Europe C) Since at least the period of ancient Babylon in the 17th century BCE D) Since the invention of digital computers
A) One B) Five C) Three D) Ten
A) A prime number B) A hypotenuse C) A cube's volume D) A circle's area
A) The last manual square root method B) An exact formula for irrational numbers C) The first ascertainable algorithm for computing square root D) The first digital computer program
A) In the 21st century B) After introduction of the Arabic numeral system to western Europe C) During the ancient Babylonian period D) During the construction of the Egyptian pyramids
A) Western Europe in the early Renaissance B) South America in pre-Columbian times C) East Asia in the Middle Ages D) Ancient Mesopotamia
A) As a language construct, compiler intrinsic, library function, or hardware operator B) Using paper and pencil simulation C) Exclusively via continued fractions D) Only through manual user input
A) Any real number B) A non-zero positive number C) Zero D) A negative number
A) Faster convergence B) Higher memory usage C) Slower convergence D) More required iterations
A) It converges much slower B) It converges slightly faster C) It converges at the exact same speed D) It does not converge at all
A) a <= 1 B) a < 10 C) a < 1000 D) a < 100
A) Into logarithmic scales only B) Into negative domains C) Into intervals D) Into infinite continuous curves
A) 6.0 B) 4.0 C) 5.5 D) 3.16
A) a = 10 B) a = 5.5 C) a = 100 D) a = 1
A) 50% B) 10% C) 4% D) 100%
A) Least-squares regression line B) Exponential curve C) Horizontal asymptote D) Vertical median
A) 30% B) 50% C) 17% D) 10%
A) Constant rounding B) Piece-wise linear approximation C) Logarithmic interpolation D) Cubic spline extrapolation
A) Use tangent lines B) Use quadratic polynomials C) Use random sampling D) Use secant lines exclusively
A) 372.8 B) 354.0 C) 256 D) 125348
A) 3.0 B) 5.3 C) 0.086 D) 19
A) 8 bits B) 2 bits C) 16 bits D) 4+ bits
A) The sign bit B) The exponent C) The low bit D) The high bit
A) 64 bytes B) 256 bytes C) 128 bytes D) 512 bytes
A) 11101001_2 B) 11101101_2 C) 10101110_2 D) 0100_2
A) 11101101_2 B) 10101110_2 C) 01101011_2 D) 11101001_2
A) A first-century Greek mathematician B) A twelfth-century Greek philosopher C) A sixth-century Babylonian king D) A modern computer scientist
A) Elements B) Metrica C) Arithmetica D) Almagest
A) 60 BC B) AD 600 C) 160 AD D) AD 60
A) Yes, recorded by Babylonian astronomers B) Yes, extensive clay tablets exist C) No evidence exists D) Yes, mentioned in Babylonian poetry
A) Quadratically convergent B) Linearly convergent C) Cubically convergent D) Logarithmically convergent
A) Quaternions B) Imaginary numbers C) Complex numbers D) p-adic numbers
A) 400 B) 600 C) 1000 D) 350
A) 404.456666666 B) 357.1868 C) 354.0452 D) 600.0
A) 357.186837334 B) 354.0590 C) 404.456666666 D) 600.0
A) Seven B) Ten C) Five D) Fifteen
A) 6 B) 28 C) 23 D) 22
A) 28 B) 6 C) 22 D) 23
A) 23 B) 6 C) 22 D) 28
A) sqrt_Newton B) sqrt_Heron C) sqrt_p_adic D) sqrt_approximate
A) The true square root value B) The absolute error C) The difference between successive estimates D) The convergence constant
A) When the successive differences become sufficiently small B) When delta_n equals the true value S C) When C is greater than 1 D) When the absolute error is zero
A) Quartically B) Quadratic C) Linear D) Cubic
A) Triples B) Roughly quadruples C) Roughly doubles D) Increases by one
A) -199.5433 B) -190.5433 C) -195.5433 D) -195.4533
A) -195 B) -200 C) -196 D) -205
A) 600 B) 350 C) 400 D) 450
A) 354 B) 600 C) 400 D) 350
A) 354.06857 B) 354.60857 C) 355.06857 D) 350.06857
A) 354.045194 B) 350.045194 C) 354.450194 D) 354.06857
A) 8 digits B) 6 digits C) 4 digits D) 10 digits
A) Napier B) François Viète C) Babylonians D) Isaac Newton
A) No, only base 10 B) Yes C) No, only base 16 D) No, only base 2
A) A slide rule B) Napier's bones C) An abacus D) A Pascaline
A) 11 B) 00 C) Nothing D) The decimal point
A) x(p + x) <= c B) 20px <= c C) x(20p + x) <= c D) x(10p + x) <= c
A) 20p + x B) c - x C) p squared D) x(20p + x)
A) Old p times 20 plus x B) Old p plus x C) x times 10 plus p D) Old p times 10 plus x
A) Add y to c B) Multiply c by y C) Divide c by y D) Subtract y from c
A) 13.24 B) 12.34 C) 11.45 D) 15.22
A) It requires more storage space than lookup tables B) It converges very slowly compared to other methods C) Numerical errors accumulate D) It cannot be implemented on fixed-point hardware
A) 1940 B) 1960 C) 1950 D) 1975
A) EDSAC B) UNIVAC I C) ENIAC D) Manchester Baby
A) Babylonian scholars B) Isaac Newton C) Edmond Halley D) Robert Elliot Goldschmidt
A) 17 divided by 12 B) 99 divided by 70 C) 41 divided by 29 D) 5 divided by 2
A) Quadratic irrationals B) Remainders C) Convergents D) Denominators
A) 01 B) 00 C) 10 D) 11
A) The natural logarithm B) The base-2 logarithm C) The base-10 logarithm D) The exponential function
A) 0x3F800000 B) 0x00000001 C) 0x4B0D2000 D) 0x3FC00000
A) 1056964608 B) 2130706432 C) 1065353216 D) 524288
A) 0x3F800000 B) 0x1FBB4F2E C) 0x3FC00000 D) 0xFC00000
A) The number of bits in the mantissa B) The exponent bias C) The base of the logarithm D) The error adjustment constant |