What is 11 -2/11 plz answer this
2 answers:
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Answer:
c. 8 units
Step-by-step explanation:
You are to find the y-intercepts of the two functions given, then report the difference between them. The y-intercept is the y-value when x=0.
For f(x), we have ...
f(0) = 3·2^0 = 3·1 = 3
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For the table, we can see that x=0 is halfway between x=-2 and x=2, so the y-intercept can be expected to be halfway between y=3 and y=-13. That value for y is ...
g(0) = (3 + (-13))/2 = -10/2 = -5
That is, the y-intercept of g(x) is -5.
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The difference between f(0) and g(0) is ...
f(0) -g(0) = 3 -(-5) = 8 . . . . units
Answer:
Step-by-step explanation:
.
It is apparently obvious we could expand the bracket and integrate term-by-term. This method would work but is very time consuming (and you could easily make a mistake) so we use a different method: integration by substitution.
Integration by substitution involves swapping the variable for another variable which depends on x:
. (We are going to choose
for this question).
The very first step is to choose a suitable substitution. That is, an equation which is going to make the integration easier. There is a trick for spotting this however: if an integral contains both a term and it's derivative then use the substitution
.
Your integral contains the term . The derivative is
and (ignoring the constants) we see
is also in the integral and so the substitution
will unravel this integral!
Step 2: We must now swap the variable of integration from x to u. That means interchanging all the x's in the integrand (the term being integrated) for u's and also swapping (dx" to "du").
Then,
.
The substitution has made this integral is easy to solve!
Finally we can substitute back to get the answer in terms of x: