immediately please tell me this question's answer

Asked by akankhyapradhan123 | 18th Jan, 2022, 06:16: AM

Expert Answer:

To find the limit
limit as straight x rightwards arrow square root of 3 of space open parentheses fraction numerator straight x to the power of 4 minus 4 over denominator straight x squared plus 3 square root of 2 straight x minus 8 end fraction close parentheses
equals limit as straight x rightwards arrow square root of 3 of space open parentheses fraction numerator open parentheses straight x squared minus 2 close parentheses open parentheses straight x squared plus 2 close parentheses over denominator straight x squared plus 4 square root of 2 straight x minus square root of 2 straight x minus 8 end fraction close parentheses
equals limit as straight x rightwards arrow square root of 3 of space open parentheses fraction numerator open parentheses straight x minus square root of 2 close parentheses open parentheses straight x plus square root of 2 close parentheses open parentheses straight x squared plus 2 close parentheses over denominator open parentheses straight x plus 4 square root of 2 close parentheses straight x minus square root of 2 open parentheses straight x plus 4 square root of 2 close parentheses end fraction close parentheses
equals limit as straight x rightwards arrow square root of 3 of space open parentheses fraction numerator open parentheses straight x minus square root of 2 close parentheses open parentheses straight x plus square root of 2 close parentheses open parentheses straight x squared plus 2 close parentheses over denominator open parentheses straight x plus 4 square root of 2 close parentheses open parentheses straight x minus square root of 2 close parentheses end fraction close parentheses
equals limit as straight x rightwards arrow square root of 3 of space open parentheses fraction numerator open parentheses straight x plus square root of 2 close parentheses open parentheses straight x squared plus 2 close parentheses over denominator open parentheses straight x plus 4 square root of 2 close parentheses end fraction close parentheses
equals fraction numerator 5 open parentheses square root of 3 plus square root of 2 close parentheses over denominator square root of 3 plus 4 square root of 2 end fraction

Answered by Renu Varma | 18th Jan, 2022, 01:09: PM