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### 3.7 Answers to Exercises

This section includes answers to all the exercises in the Calc tutorial.

- RPN Answer 1: 1 <RET> 2 <RET> 3 <RET> 4 + * -
- RPN Answer 2: 2*4 + 7*9.5 + 5/4
- RPN Answer 3: Operating on levels 2 and 3
- RPN Answer 4: Joe's complex problems
- Algebraic Answer 1: Simulating Q command
- Algebraic Answer 2: Joe's algebraic woes
- Algebraic Answer 3: 1 / 0
- Modes Answer 1: 3#0.1 = 3#0.0222222?
- Modes Answer 2: 16#f.e8fe15
- Modes Answer 3: Joe's rounding bug
- Modes Answer 4: Why floating point?
- Arithmetic Answer 1: Why the \ command?
- Arithmetic Answer 2: Tripping up the B command
- Vector Answer 1: Normalizing a vector
- Vector Answer 2: Average position
- Matrix Answer 1: Row and column sums
- Matrix Answer 2: Symbolic system of equations
- Matrix Answer 3: Over-determined system
- List Answer 1: Powers of two
- List Answer 2: Least-squares fit with matrices
- List Answer 3: Geometric mean
- List Answer 4: Divisor function
- List Answer 5: Duplicate factors
- List Answer 6: Triangular list
- List Answer 7: Another triangular list
- List Answer 8: Maximum of Bessel function
- List Answer 9: Integers the hard way
- List Answer 10: All elements equal
- List Answer 11: Estimating pi with darts
- List Answer 12: Estimating pi with matchsticks
- List Answer 13: Hash codes
- List Answer 14: Random walk
- Types Answer 1: Square root of pi times rational
- Types Answer 2: Infinities
- Types Answer 3: What can "nan" be?
- Types Answer 4: Abbey Road
- Types Answer 5: Friday the 13th
- Types Answer 6: Leap years
- Types Answer 7: Erroneous donut
- Types Answer 8: Dividing intervals
- Types Answer 9: Squaring intervals
- Types Answer 10: Fermat's primality test
- Types Answer 11: pi * 10^7 seconds
- Types Answer 12: Abbey Road on CD
- Types Answer 13: Not quite pi * 10^7 seconds
- Types Answer 14: Supercomputers and c
- Types Answer 15: Sam the Slug
- Algebra Answer 1: Squares and square roots
- Algebra Answer 2: Building polynomial from roots
- Algebra Answer 3: Integral of x sin(pi x)
- Algebra Answer 4: Simpson's rule
- Rewrites Answer 1: Multiplying by conjugate
- Rewrites Answer 2: Alternative fib rule
- Rewrites Answer 3: Rewriting opt(a) + opt(b) x
- Rewrites Answer 4: Sequence of integers
- Rewrites Answer 5: Number of terms in sum
- Rewrites Answer 6: Truncated Taylor series
- Programming Answer 1: Fresnel's C(x)
- Programming Answer 2: Negate third stack element
- Programming Answer 3: Compute sin(x) / x, etc.
- Programming Answer 4: Average value of a list
- Programming Answer 5: Continued fraction phi
- Programming Answer 6: Matrix Fibonacci numbers
- Programming Answer 7: Harmonic number greater than 4
- Programming Answer 8: Newton's method
- Programming Answer 9: Digamma function
- Programming Answer 10: Unpacking a polynomial
- Programming Answer 11: Recursive Stirling numbers
- Programming Answer 12: Stirling numbers with rewrites