limitx→aa+2x13-3x133a+x13-4x13=
2943
2343
232943
292313
Explanation for Correct Answer:
Evaluating the given function:
limitx→aa+2x13-3x133a+x13-4x13=limitx→aa+2a13-3a133a+a13-4a13=limitx→a3a13-3a134a13-4a13=00
00 indeterminant form using L Hospitals rule.
limitx→aa+2x13-3x133a+x13-4x13=limitx→a13a+2x-23.2-133x-23.3133a+x-23-134x-23.4∵ddxxn=nxn-1=limitx→a132.a+2x-23-3.3x-23133a+x-23-4.4x-23
=2.a+2a-23-3.3a-233a+a-23-4.4a-23=2.3a-23-3.3a-234a-23-4.4a-23=-1.3-23a-23-3.4-23a-23
=1.3-233.22-23=13.34-23=13.43213∵a-1=1a=13.16913=13.8×2913=23.2913∵813=2
Hence, the correct answer is option (C).
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