Unsure how to solve these calculus limits numerically:

Question

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

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

Answer 1

1)

  lim    (3^h -1)/h

h--->0

Use formula:

lim    (a^x -1)/x    =  log_e a

x--->0

So  lim    (3^h -1)/h  = log_e 3

     h--->0

Answer 2

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