Answer:
(e) csc x − cot x − ln(1 + cos x) + C
(c) 0
Step-by-step explanation:
(e) ∫ (1 + sin x) / (1 + cos x) dx
Split the integral.
∫ 1 / (1 + cos x) dx + ∫ sin x / (1 + cos x) dx
Multiply top and bottom of first integral by the conjugate, 1 − cos x.
∫ (1 − cos x) / (1 − cos²x) dx + ∫ sin x / (1 + cos x) dx
Pythagorean identity.
∫ (1 − cos x) / (sin²x) dx + ∫ sin x / (1 + cos x) dx
Divide.
∫ (csc²x − cot x csc x) dx + ∫ sin x / (1 + cos x) dx
Integrate.
csc x − cot x − ln(1 + cos x) + C
(c) ∫₋₇⁷ erf(x) dx
= ∫₋₇⁰ erf(x) dx + ∫₀⁷ erf(x) dx
The error function is odd (erf(-x) = -erf(x)), so:
= -∫₀⁷ erf(x) dx + ∫₀⁷ erf(x) dx
= 0
Answer: 4/2
Step-by-step explanation: Rise over run. From point S to R it goes up 4 and over 2.
Answer:
A) arithmetic sequence
g(n) = 20 + 3n
Step-by-step explanation:
Each minute, the number of pages increases by 3, which means the common difference is 3 (because it is being added, not multiplied).
If there is a common difference, it's an arithmetic sequence. (Geometric sequences have common ratios.)
If she starts at 20 pages, then you just need to multiply 3 by the number of minutes passed (n) and add it to 20 to find the page she's on.
No unless they are near each other and it says they are together ........
