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3. (10 marks) Find the limit and prove it using the definition. 4x2 + 13 lim x2 + x +1 X-700

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lim 4x²+13 x²+x+1 lim 4+ 13 x2 ( Dividing both N and D x 500 It + ㅗ X2 by x²) uto toyo = 4 By definition Since lim 4x²+13 =4As & is very is very large 9-4x co =) 279 4 19-uul 4x-9 =) 4u-a 40²13 22x2 ५ 4 2+2+1 Let 42-9 =k x+x+1 Now we find the maximuK = ? (J133 -11) k z 2 3 į (-133-11) (K-2) CK-B)LO ( from (1)) ask & ß where ß = 2 (J13-11) and a= V 4X-9 x24041 < (J133-11)

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