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Unsure how to solve these calculus limits numerically:

0 votes

1)Limit as h approaches 0 of (3^h-1)/(h)

2)Limit as h approaches 0 of (cosh-1)/(h)?

asked Sep 16, 2014 in PRECALCULUS by anonymous

2 Answers

0 votes

1)

  lim    (3^h -1)/h

h--->0

Use formula:

lim    (a^x -1)/x    =  loge a

x--->0

So  lim    (3^h -1)/h  = loge 3

     h--->0

answered Sep 16, 2014 by bradely Mentor
0 votes

2)

  lim    (cosh -1)/h

h--->0

Write down the the expansion of cos h

cos h =1 - (h²/2)

  lim    (1 - (h²/2) -1)/h

h--->0

lim    (h²/2)/h

h--->0

lim    (h/2)    = 0

h--->0

answered Sep 16, 2014 by bradely Mentor

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