Note that √(4 - t²) is defined only as long as 4 - t² ≥ 0, or -2 ≤ t ≤ 2. Then the real integral exists only if -2 ≤ x ≤ 2. (Otherwise we deal with complex numbers.)
If x = 2, then the integral corresponds to the area of a quarter-circle with radius 2. This means that the integral has a maximum value of 1/4 • π • 2² = π.
On the opposite end, if x = -2, then the integral has the same value, but the integral from 0 to -2 is equal to the negative integral from -2 to 0. So the minimum value is -π.
For all x in between, we observe that the integrand is continuous over the rest of its domain, so F(x) is continuous.
Then the range of F(x) is the interval [-π, π].
A lot of teachers don't teach SohCahToa anymore! this acronym will really help you. I'd suggest looking up how to use it, it'll make trigonometry WAY easier!
Answer:
infinitely many solutions
Step-by-step explanation:
0 = 0 ← is a true statement.
Indicates that the 2 lines are the same line, that is one lying on top of the other.
Thus the system has an infinite number of solutions
A fraction with a numerator that is greater than or equal to the denominator is known as an improper fraction.
Answer:
50+0.03x
Step-by-step explanation:
All you need to do is look at the numbers given in the word problem and convert them to algebraic terms.
