$SPAD/src/input explim.input

Clifton J. Williamson and Timothy Daly

December 3, 2016

Abstract

Contents

2

1 License

— license —

--Copyright The Numerical Algorithms Group Limited 1991.

———-

— * —

)set break resume
)spool explim.output
)set message test on
)set message auto off
)clear all

———-

2 Limits involving essential singularities of the exponential function

Some of these limits were taken from bug reports submitted before additions and changes were made to limit and related series packages.

— * —

)clear all
--S 1 of 12
limit(x/exp(x),x = %plusInfinity)              -- 0
--R
--R
--R   (1)  0
--R                      Type: Union(OrderedCompletion(Expression(Integer)),...)
--E 1
--S 2 of 12
limit(x**10000/exp(x),x = %plusInfinity)       -- 0
--R
--R
--R   (2)  0
--R                      Type: Union(OrderedCompletion(Expression(Integer)),...)
--E 2
--S 3 of 12
limit(x**(10**20)/exp(x),x = %plusInfinity)    -- 0
--R
--R
--R   (3)  0

--R                      Type: Union(OrderedCompletion(Expression(Integer)),...)
--E 3
--S 4 of 12
limit(x**h/exp(x),x = %plusInfinity)           -- 0
--R
--R
--R   (4)  0
--R                      Type: Union(OrderedCompletion(Expression(Integer)),...)
--E 4
--S 5 of 12
limit(x/exp(x),x = %minusInfinity)             -- %minusInfinity
--R
--R
--R   (5)  - infinity
--R                      Type: Union(OrderedCompletion(Expression(Integer)),...)
--E 5
--S 6 of 12
limit(x**10000/exp(x),x = %minusInfinity)      -- %plusInfinity
--R
--R
--R   (6)   + infinity
--R                      Type: Union(OrderedCompletion(Expression(Integer)),...)
--E 6
--S 7 of 12
limit(x**(10**20)/exp(x),x = %minusInfinity)   -- %plusInfinity
--R
--R
--R   (7)   + infinity
--R                      Type: Union(OrderedCompletion(Expression(Integer)),...)
--E 7
--S 8 of 12
limit(x**h/exp(x),x = %minusInfinity)          -- "failed"
--R
--R
--R   (8)  "failed"
--R                                                    Type: Union("failed",...)
--E 8
--S 9 of 12
limit(exp(-x) * sinh(x),x = %plusInfinity)     -- 1/2
--R
--R
--R        1
--R   (9)  -
--R        2

--S 10 of 12
limit(exp(-x) * cosh(x),x = %plusInfinity)     -- 1/2
--R
--R
--R         1
--R   (10)  -
--R         2
--R                      Type: Union(OrderedCompletion(Expression(Integer)),...)
--E 10
--S 11 of 12
limit(exp(-x) * exp(x),x = %plusInfinity)      -- 1
--R
--R
--R   (11)  1
--R                      Type: Union(OrderedCompletion(Expression(Integer)),...)
--E 11
--S 12 of 12
limit((x + 1)**(x + 1)/x**x - x**x/(x - 1)**(x - 1),x = %plusInfinity)  -- %e
--R
--R
--R   (12)  %e
--R                      Type: Union(OrderedCompletion(Expression(Integer)),...)
--E 12
)spool
)lisp (bye)

———-

References^{[1] nothing}

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