Answer:
D.
Step-by-step explanation:
Not for sure sorry but i think its D or A so so sorry
-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29
7-12= -5
7+12= 29
-5 ≤ n ≤ 29 or -5 ≤ n < 30 or -6< n ≤ 29 or -6 < n < 30
either one is acceptable. question was not clear but i did my best! :)
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π − 12
lim(x→2) (sin(πx) + 8 − x³) / (x − 2)
If we substitute x = u + 2:
lim(u→0) (sin(π(u + 2)) + 8 − (u + 2)³) / ((u + 2) − 2)
lim(u→0) (sin(πu + 2π) + 8 − (u + 2)³) / u
Distribute the cube:
lim(u→0) (sin(πu + 2π) + 8 − (u³ + 6u² + 12u + 8)) / u
lim(u→0) (sin(πu + 2π) + 8 − u³ − 6u² − 12u − 8) / u
lim(u→0) (sin(πu + 2π) − u³ − 6u² − 12u) / u
Using angle sum formula:
lim(u→0) (sin(πu) cos(2π) + sin(2π) cos(πu) − u³ − 6u² − 12u) / u
lim(u→0) (sin(πu) − u³ − 6u² − 12u) / u
Divide:
lim(u→0) [ (sin(πu) / u) − u² − 6u − 12 ]
lim(u→0) (sin(πu) / u) + lim(u→0) (-u² − 6u − 12)
lim(u→0) (sin(πu) / u) − 12
Multiply and divide by π.
lim(u→0) (π sin(πu) / (πu)) − 12
π lim(u→0) (sin(πu) / (πu)) − 12
Use special identity, lim(x→0) ((sin x) / x ) = 1.
π (1) − 12
-99
