SOLUTION: The calculation of lim 5x + 5h + 1 - (5x + 1)/h h -> 0

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Question 637331: The calculation of lim 5x + 5h + 1 - (5x + 1)/h

h -> 0
Found 2 solutions by ewatrrr, jsmallt9:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Curious to know where the  5x + 5h + 1 - (5x + 1) came from.

If You meant:

lim%28h-%3E0%2C+%28%285x%2B5h%2B1%29-%285x%2B1%29%29%2Fh%29

lim%28h-%3E0%2C+%285h%29%2Fh%29+=+5

Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
I'm going to assume that your problem is
lim%28h-%3E0%2C+%28%285x%2B5h%2B1%29-%285x%2B1%29%29%2Fh%29
(Please use parentheses to make your expressions clearer.)

Let's simplify the fraction. In the numerator, the 5x's and the 1's cancel out:
lim%28h-%3E0%2C+%285h%29%2Fh%29

Next we could cancel the h's, but only if h is not zero! An important thing to understand about this limit is that we are interested in what happens when h gets infinitely close to zero but not actually zero. Since h is never actually zero, it is OK to cancel the h's:
lim%28h-%3E0%2C+5%29
And since the limit of a constant is that constant, this simplifies to just
5

So lim%28h-%3E0%2C+%28%285x%2B5h%2B1%29-%285x%2B1%29%29%2Fh%29+=+5