Limits doubt

q31

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Wait

Please post clear nd which is not inverted i was confused i thought \lim_{\ n\ to \infty}
Please take common last term apply limt ans will be n

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q33 also

Since its infinity by infinity form.....so start diffrentiating numerator and denominator....since numerator is alzebric fn hence after some time it would completely be diffrentiated whereas denominator is e^x which remains same after any no of diifrentiation .....hence nume will be some.finite ni whereas denominator will be infinite hence ans is zero

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Ans is zero
[x] \approx {\infty}
When x \rightarrow \infty
Why u apply l opital n time numerator can become n! but lower limt will be infinity only

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