Answer: cool!
Step-by-step explanation: ;)
First substitute to rewrite the integral as
Now use an Euler substitution, to rewrite it again as
where we take
Partial fractions:
so that
The second integral is trivial,
For the other, I'm compelled to use the residue theorem, though real methods are doable too (e.g. trig substitution). Consider the contour integral
where is a semicircle in the upper half of the complex plane, and its diameter lies on the real axis connecting to . The value of this integral is 2πi times the sum of the residues in the upper half-plane. It's fairly straightforward to convince ourselves that the integral along the circular arc vanishes as , so the contour integral converges to the integral over the entire real line. Note that
since the integrand is even.
Find the poles of .
where .
The two poles we care about are at and . Compute the residues at each one.
By the residue theorem,
We also have
Then the remaining integral is
It follows that
First of all, recall that division by zero is undefined; it's nonsensical; it's just not allowed.So zero certainly needs to be excluded when dividing.
But what about multiplying by zero?
The problem is that multiplying by zero can change the truth of an equation:
It can take a false equation to a true equation.
To see this, consider the false equation ‘
2 = 3
Multiplying both sides by zero results in the new equation
2 ⋅ 0 = 3 ⋅0 (that is, ‘0 = 0’), which is true.
Answer:
The circumference of the circle is about 226.08 inches. ANSWER: 3.14 × 72 = 226.08 in.
Step-by-step explanation:
Answer:
f(7) = -113
Step-by-step explanation:
Hello!
Substitute 7 for x in the equation.
<h3>Evaluate</h3>
- f(x) = -4x² + 10x + 13
- f(7) = -4(7)² + 10(7) + 13
- f(7) = -4(49) + 70 + 13
- f(7) = -196 + 70 + 13
- f(7) = -113
f(7) is -113.