10 Questions packed into one Question

Calculus Level pending

For statements that is correct, type 1. For statements that is incorrect, type 2. For statements that is partially correct, type 3. So the answer is a 10-digit number 1) 27 3 9 = 0 \sqrt [ 3 ]{ 27 } \quad -\quad \sqrt { 9 } \quad =\quad 0 2) log 10 × log 100 = log 1000 \log { 10 } \quad \times \quad \log { 100 } \quad =\quad \log { 1000 } 3) x 2 2 x 3 = 0 { x }^{ 2 }\quad -\quad 2x\quad -\quad 3\quad =\quad 0 has the factors x = 1 x\quad =\quad -1 and x = 3 x\quad =\quad 3 4) 999 999 { 999 }^{ 999 } is divisible by 3 5) Since 10 ! 10! has 2 trailing zeros, and 20 ! 20! has 4 trailing zeros, 10 ! + 20 ! 10! + 20! has 6 trailing zeros 6) s i n 2460 = s i n 300 sin\quad { 2460 }^{ \circ }\quad =\quad sin\quad { 300 }^{ \circ } 7) If f ( x ) = a x + b c x + d f\left( x \right) \quad =\quad \frac { ax\quad +\quad b }{ cx\quad +\quad d } , then f 1 ( x ) = d x + b c x a f^{ -1 }\left( x \right) \quad =\quad \frac { -dx\quad +\quad b }{ cx\quad -\quad a } 8) x 4 × x 4 = x \sqrt [ 4 ]{ x } \quad \times \quad \sqrt [ 4 ]{ x } \quad =\quad \sqrt { x } 9) lim n 1 n 2 1 n 1 = 2 \lim _{ n\quad \rightarrow \quad 1 }{ \frac { { n }^{ 2 }\quad -\quad 1 }{ n\quad -\quad 1 } } \quad =\quad 2 10) 10 10 log 10 10 = 5 2 π \frac { \sqrt [ 10 ]{ 10 } }{ \log _{ 10 }{ 10 } } \quad =\quad \frac { 5 }{ 2 } \pi


The answer is 3221221112.

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