What is the domain of the following functions
1 answer:
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Answer:
- f'(1) exists: f'(1) = -2
- f'(0) DNE
Step-by-step explanation:
<h3>a)</h3>The function is continuous for x > 0 . The derivative is defined on that interval and is equal to ...
f'(x) = -2x . . . . . for x > 0
Then at x = 1, the derivative is ...
f'(1) = -2(1)
f'(1) = -2
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<h3>b)</h3>The function has a jump discontinuity at x=0, so the derivative does not exist at that point. A condition for the existence of the derivative is that the function is continuous at the point of interest.
I am attaching the full question...
Because AB is parallel to CD, the transversal line EF creates the same angles in AB and CD.
This means that 3x+40 = 4x
..........==>> x = 40 degrees
Because AB is parallel to CD, the transversal line EF creates the same angles in AB and CD.
This means that 3x+40 = 4x
..........==>> x = 40 degrees
Answer:
The sum of the first 20 terms is -1440.
Step-by-step explanation:
We want to find the sum of the first 20 terms of the arithmetic sequence:
4, -4, -12, -20...
The sum of an arithmetic sequence is given by:
Where <em>k</em> is the number of terms, <em>a</em> is the initial term, and <em>x</em>_<em>k</em> is the last term.
Since we want to find the sum of the first 20 terms, <em>k</em> = 20.
Our initial term <em>a</em> is 4.
Our last term is also the 20th term as we want the sum of the first 20 terms.
To find the 20th term, we can write an explicit formula for our sequence. The explicit formula for an arithmetic sequence is given by:
Where <em>a</em> is the initial term, <em>d</em> is the common difference, and <em>n</em> is the <em>n</em>th term.
Our initial term is 4. From the sequence, we can see that our common difference is -8 since each subsequent term is eight less than the previous term. Therefore:
Then the last or 20th term is:
Therefore, the sum of the first 20 terms are: