Given that the limit of f(x)/x as x approaches 0 is 3, find the limit of f((x^3)-1)/(x-1) as x approaches 1.
I have been stuck on this for a while now.
I don't want the answer, I just want to understand how to solve this problem.
Thanks.
I have been stuck on this for a while now.
I don't want the answer, I just want to understand how to solve this problem.
Thanks.
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Given : lim (x→0) [ ƒ(x) / x ] = 3 ................. (1)
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∴ lim (x→1) [ ƒ(x³-1) / (x-1) ]
= lim (x→1) [ ƒ(x³-1) / (x³-1) ] • [ (x³-1) / (x-1) ] ...... Note This Step
= lim (X→0) [ ƒ(X) / X ] · lim (x→1) (x²+x+1), ........ X = (x-1) → 0
= 3 · ( 1² + 1 + 1 ) ..................... from (1)
= 9 ........................................… Ans.
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Happy To Help !
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∴ lim (x→1) [ ƒ(x³-1) / (x-1) ]
= lim (x→1) [ ƒ(x³-1) / (x³-1) ] • [ (x³-1) / (x-1) ] ...... Note This Step
= lim (X→0) [ ƒ(X) / X ] · lim (x→1) (x²+x+1), ........ X = (x-1) → 0
= 3 · ( 1² + 1 + 1 ) ..................... from (1)
= 9 ........................................… Ans.
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Happy To Help !
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Of course it is Sir !
See my name ?
Not just Hemant but ... He-Man-T !!!
See my name ?
Not just Hemant but ... He-Man-T !!!
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