Show that 3x 4 + 1 is o(x 4/2) and x 4/2 is o(3x 4 + 1)

1.	Show that 3x 4 + 1 is o(x 4/2) and x 4/2 is o(3x 4 + 1)
Answer» SOLUTION TO PROVE $\displaystyle\sf{3 {x}^{4} + 1 = O \bigg( \frac{ {x}^{4} }{2} \bigg) \: \: \: and \: \: \: \frac{ {x}^{4} }{2}= O \bigg( 3 {x}^{4} + 1 \bigg)}$ CONCEPT TO BE IMPLEMENTED If f(x) & g(x) are two real valued function then f(x) = O(g(x)) if there exists a non ZERO real NUMBER c such that f(x) ≤ c g(x) PROOF $\displaystyle\sf{3 {x}^{4} + 1 }$ $\displaystyle\sf{ \leqslant 3 {x}^{4} + {x}^{4} }$ $\displaystyle\sf{ = 4 {x}^{4} }$ $\displaystyle\sf{ = 8. \frac{ {x}^{4} }{2} }$ $\displaystyle\sf{ \therefore \: \: 3 {x}^{4} + 1 = O \bigg( \frac{ {x}^{4} }{2} \bigg) \:}$ Again $\displaystyle\sf{\frac{ {x}^{4} }{2}}$ $\displaystyle\sf{ = \frac{1}{6}.3 {x}^{4} }$ $\displaystyle\sf{ \leqslant \frac{1}{6} \bigg( 3 {x}^{4} + 1 \bigg) }$ $\displaystyle\sf{ \therefore \: \: \frac{ {x}^{4} }{2}= O \bigg( 3 {x}^{4} + 1 \bigg)}$ Hence proved ━━━━━━━━━━━━━━━━ Learn more from Brainly :- 1. write the expression for gradient and DIVERGENCE brainly.in/question/32412615 2. prove that the CURL of the gradient of (scalar function) is zero brainly.in/question/19412715

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