Divided by let's factor out an x out of the numerator.

Let's factor out an x squared out of the numerator and the denominator.

God increases the means of those of His creatures as He please , or limits them for whomsoever He will . He is certainly cognisant of everything .

Allah eases the sustenance for whomever He wills among His bondmen , and restricts it for whomever He wills indeed Allah knows all things .

God outspreads and straitens His provision to whomsoever He will of His servants God has knowledge of everything .

Allah expandeth provision for whomsoever He Will of His bondmen and stinteth it for him . Verily Allah is of everything the Knower .

Allah enlarges the provision for whom He wills of His slaves , and straitens it for whom ( He wills ) . Verily , Allah is the All Knower of everything .

God expands the provision for whomever He wills of His servants , and restricts it . God is Cognizant of all things .

Allah enlarges the sustenance of any of His servants whom He will , and straitens the sustenance of whom He will . Surely Allah has knowledge of everything .

Allah maketh the provision wide for whom He will of His bondmen , and straiteneth it for whom ( He will ) . Lo !

Allah expands the provision for whomever He wishes of His servants , and tightens it for him . Indeed Allah has knowledge of all things .

Allah outspreads and restricts His provision to whomsoever He will of His worshipers . Allah has knowledge of all things .

Allah extends provision for whom He wills of His servants and restricts for him . Indeed Allah is , of all things , Knowing .

God increases the sustenance of whichever of His servants He wants and He determines their share . God has the knowledge of all things .

Allah makes abundant the means of subsistence for whom He pleases of His servants , and straitens them for whom ( He pleases ) surely Allah is Cognizant of all things .

God gives abundantly to whom He will and sparingly to whom He pleases . God has full knowledge of all things .

Allah enlarges the sustenance ( which He gives ) to whichever of His servants He pleases and He ( similarly ) grants by ( strict ) measure , ( as He pleases ) for Allah has full knowledge of all things .

In the second step, they were divided by 3.

And once again, when you evaluated infinity, the numerator is going to approach infinity.

The main derived quantity in which amount of substance enters into the numerator is amount of substance concentration, c .

That the numerator approaches infinity as x approaches infinity.

So if you were to just kind of evaluate it at infinity, the numerator, you would get positive infinity.

So the derivative of the numerator is the derivative of 4x squared is 8x minus 5 over the derivative of the denominator is, well, derivative of 1 is 0.

That way, the debt GDP ratio declines because the denominator (economic output) increases, not because the numerator (the total the government has borrowed) declines.

Examples of proper fractions are 2 3, 3 4, and 4 9 examples of improper fractions are 9 4, 4 3, and 3 3.

So if this limit exists, or if the limit of their derivatives exist, then this limit's going to be equal to the limit as x approaches infinity of the derivative of the numerator.

Do not be niggardly , nor extravagant that you may later feel reprehensive and constrained .

And do not keep your hand tied to your neck nor open it completely , lest you remain seated reproached , weary .

And keep not thy hand chained to thy neck , nor outspread it widespread altogether , or thou wilt sit reproached and denuded .

And let not thine hand be chained to thy neck , nor stretch it forth to the utmost stretching , lest thou sit down reproached , impoverished .

And let not your hand be tied ( like a miser ) to your neck , nor stretch it forth to its utmost reach ( like a spendthrift ) , so that you become blameworthy and in severe poverty .

And do not keep your hand tied to your neck , nor spread it out fully , lest you end up liable and regretful .

( vi ) Do not keep your hand fastened to your neck nor outspread it , altogether outspread , for you will be left sitting rebuked , destitute .

And let not thy hand be chained to thy neck nor open it with a complete opening , lest thou sit down rebuked , denuded .

Do not keep your hand chained to your neck , nor open it altogether , or you will sit blameworthy and regretful .

And do not keep your hand chained to your neck ( when spending ) , nor open it completely , so that you will sit blamed and destitute .

And do not make your hand as chained to your neck or extend it completely and thereby become blamed and insolvent .

Do not be stingy nor over generous lest you become empty handed and bankrupt .

And do not make your hand to be shackled to your neck nor stretch it forth to the utmost ( limit ) of its stretching forth , lest you should ( afterwards ) sit down blamed , stripped off .

Be neither miserly , nor so open handed that you suffer reproach and become destitute .

Make not thy hand tied ( like a niggard 's ) to thy neck , nor stretch it forth to its utmost reach , so that thou become blameworthy and destitute .

So I ask, What would move T, technology, from the numerator call it T1 where it increases impact, to the denominator call it T2 where it reduces impact?

But some of it comes from countries where growth was already slow, and thus where high debt GDP ratios, as Larry Summers constantly says, result from the denominator, not the numerator.

But if you wanted to evaluate this limit, what you might try to do is just evaluate if you want to find the limit as this numerator approaches infinity, you put in really large numbers there, and you're going to see that it approaches infinity.

If God were to give in abundance to His creatures they would fill the earth with oppression . So He gives according to measure as He will .