How can we evaluate the limit as X approaches infinity for this expression x squared over E raised to the X well we could try direct substitution so if we replace X with infinity squared is basically infinity and areas to the infinity is infinity now this is an indeterminate form what is infinity divided by infinity is it 1 is it is infinity we don't know so when you get into a situation like this you need to use l'hospital's rule and the basic idea of l'hospital's rule is this the limit as X approaches some number C of f of X over G of X is equal to the limit as X approaches C of f prime of X divided by G prime of X so basically what we can do is turn F into F Prime and G into G Prime we could do so by taking the derivative of the top and the bottom separately and then maybe we can simplify it into a form that we can get the answer so the derivative of x squared is 2x and the derivative of e 3x will remain the same now if we use direct substitution we still won't get the right answer it will still be an indeterminate form, so we need to do it again the derivative of 2x is 2 and e 3x will stay the same now at this point we can use their X substitution, so Ethan infinity is infinity and whenever you have a fixed number divided by an infinite number you're going to get zero and each time you have a bottom-heavy expression where the denominator is very high compared to the numerator this will give you 1 divided by a large number will give you a very small number...
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Form 10F is an official document that is required to be submitted by individuals who are non-resident in India and wish to apply for a certificate of residence for the purposes of claiming tax benefits under the Double Taxation Avoidance Agreement (DTAA). The following information is required to be filled in Form 10F: 1. Personal details: Name, address, and contact information of the taxpayer. 2. Taxpayer identification: Indian Permanent Account Number (PAN) or Tax Identification Number (TIN) of the taxpayer. 3. Residential status: Indication of whether the taxpayer is a resident or non-resident in India. 4. Tax treaty details: Details of the relevant tax treaty between India and the country of residence of the taxpayer. 5. Previous tax residency: Information about the taxpayer's previous tax residency status, if any. 6. Income details: Income earned in India and other countries, as well as the tax payable in each jurisdiction. 7. Tax claim details: Specific provisions of the tax treaty that the taxpayer wishes to avail for claiming tax benefits in India. 8. Address of the taxpayer in the resident country. Form 10F is required by individuals who are non-resident in India and are eligible for claiming tax benefits under the DTAA. This form needs to be submitted to the Indian income tax authorities by non-residents who wish to apply for a certificate of residence. The certificate of residence, once obtained, can be provided to the tax authorities of the resident country to claim relief under the DTAA and avoid double taxation on income.
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