10 POINTS!!! FULL ANSWER IN STEP BY STEP FORMAT!!
1 answer:
Remark
This question likely should be done before the other one. What you are trying to do is give C a value. So you need to remember that C is always part of an indefinite integral.
y =
y = sin(x) - cos(x) + C
y(π) = sin(π) - cos(π) + C = 0
y(π) = 0 -(-1) + C = 0
y(π) = 1 + C = 0
C = - 1
y = sin(x) - cos(x) - 1 <<<<< Answer
Problem Two
Remember that
y( - e^3 ) = ln(|x|) + C = 0
y(-e^3) = ln(|-e^3|) + C = 0
y(-e^3) = 3 + C = 0
3 + C = 0
C = - 3
y = ln(|x|) - 3 <<<< Answer
This question likely should be done before the other one. What you are trying to do is give C a value. So you need to remember that C is always part of an indefinite integral.
y =
y = sin(x) - cos(x) + C
y(π) = sin(π) - cos(π) + C = 0
y(π) = 0 -(-1) + C = 0
y(π) = 1 + C = 0
C = - 1
y = sin(x) - cos(x) - 1 <<<<< Answer
Problem Two
Remember that
y( - e^3 ) = ln(|x|) + C = 0
y(-e^3) = ln(|-e^3|) + C = 0
y(-e^3) = 3 + C = 0
3 + C = 0
C = - 3
y = ln(|x|) - 3 <<<< Answer
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Answer: 
Note: to write the domain in interval notation, you'd write [-4,5]
if you need the domain in set-builder notation, then you'd write
------------------------------------------------------------------------------
Explanation:
The domain is the set of possible x input values. Look at the left most point (-4,-1). The x coordinate here is x = -4. This is the smallest x value allowed. The largest x value allowed is x = 5 for similar reasons, but on the other side of the graph.
So that's how I got (x is between -4 and 5; inclusive of both endpoints)
Writing [-4,5] for interval notation tells us that we have an interval from -4 to 5 and we include both endpoints. The square brackets mean "include endpoint"
Writing is the set-builder notation way of expressing the domain. The 
portion means "x is a real number"
Note: to write the domain in interval notation, you'd write [-4,5]
if you need the domain in set-builder notation, then you'd write
------------------------------------------------------------------------------
Explanation:
The domain is the set of possible x input values. Look at the left most point (-4,-1). The x coordinate here is x = -4. This is the smallest x value allowed. The largest x value allowed is x = 5 for similar reasons, but on the other side of the graph.
So that's how I got
Writing [-4,5] for interval notation tells us that we have an interval from -4 to 5 and we include both endpoints. The square brackets mean "include endpoint"
Writing