Consider the statement: $3 \left| x ^ { 2 } \right| \leq \left| 3 x ^ { 2 } + 17 x + 5 \right| \leq 25 \left| x ^ { 2 } \right| \quad \text { for all } x 1 \text {. }$
Express this statement using $\Theta \text {-notation. }$

Question

Consider the statement: $3 \left| x ^ { 2 } \right| \leq \left| 3 x ^ { 2 } + 17 x + 5 \right| \leq 25 \left| x ^ { 2 } \right| \quad \text { for all } x > 1 \text {. }$ 
Express this statement using $\Theta \text {-notation. }$

Quizplus · Accepted Answer

The Answer of Consider the statement: $3 \left| x ^ { 2 } \right| \leq \left| 3 x ^ { 2 } + 17 x + 5 \right| \leq 25 \left| x ^ { 2 } \right| \quad \text { for all } x > 1 \text {. }$ 
Express this statement using $\Theta \text {-notation. }$

Consider the Statement 3∣x2∣≤∣3x2+17x+5∣≤25∣x2∣ for all x>1. 3 \left| x ^ { 2 } \right| \leq \left| 3 x ^ { 2 } + 17 x + 5 \right| \leq 25 \left| x ^ { 2 } \right| \quad \text { for all } x > 1 \text {. }3​x2​≤​3x2+17x+5​≤25​x2​ for all x>1.

Consider the Statement $3 \left| x ^ { 2 } \right| \leq \left| 3 x ^ { 2 } + 17 x + 5 \right| \leq 25 \left| x ^ { 2 } \right| \quad \text { for all } x > 1 \text {. }$