Limits doubt

having trouble to understand the logic behind -8-2a being 0. Also when does a limit becomes finite? is there any condition for it?
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ChaiEnjoyer
ChaiEnjoyer11mo ago
-8-2a is zero to make the limit finite
Sam
Sam11mo ago
If you want your limit to be finite.. There must be a term independent of x and all other terms must have the power of x as positive (cause if it becomes negative the limit would approach infinity which apparently isn't finite) So all the coefficients of x,x²,... Must be zero until x⁴ and more... Cause they can be zero and other powers of x can be cancelled by the x⁴ from the denominator... Suppose it weren't 0 then the term would be (-8-2a)x-² which would tend to infinity and non finite
Bhaumik_
Bhaumik_OP11mo ago
ahh ok got it thats what i was looking for , thanks +solved @Sam
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