0.1 is 10% of what number?
2 answers:
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In order to be differentiable everywhere, must first be continuous everywhere, which means the limits from either side as
must be the same and equal to
. By definition,
, and
so we need to have .
For to be differentiable at
, the derivative needs to be continuous at
, i.e.
We then need to have
Then
Answer:
Step-by-step explanation:
Ok, so we start by setting the integral up. The integral we need to solve is:
so according to the instructions of the problem, we need to start by using some substitution. The substitution will be done as follows:
U=5+x
du=dx
x=U-5
so when substituting the integral will look like this:
now we can go ahead and integrate by parts, remember the integration by parts formula looks like this:
so we must define p, q, p' and q':
p=ln U
q'=U-5
and now we plug these into the formula:
Which simplifies to:
Which solves to:
so we can substitute U back, so we get:
and now we can simplify:
notice how all the constants were combined into one big constant C.