Now we can write question 2 above in a more compact form. If the limit1limn00 nhas a value, then it is the value that should be put in the box for question 2.Question 4: Is this compact form (above), which clearly uses the symbol for infinity (in the"n → 00" part), consistent with what we understand to have been Aristotle's concept of infinity?Question 5: Does the limit1+nlimn-00nexist? If so, what is its value? If not, why not?Question 6: Does the limit(1+h)² – 1?limh→0exist? If so, what is its value? If not, why not?Optional Question 7 [only for bonus points]: Is it true that3 x3 xlimy→0_4x+ 5 ylimlimlimT0 4x +5 yWhy?B回回ロ凸 86%CHW有道 Question 1: The concept of infinity which is most often used in applications of mathematics toreal world problems is usually attributed to the ancient Greek philosopher Aristotle. What wasthis concept of infinity? Is it consistent with the fact that infinity is not now usually consideredto be a real number?Question 2: "If n increases without end, 1/n becomes closer and closer toDoes this make sense? If so, please fill in the box. Otherwise, explain the problem!Question 3: "If the positive natural number n (i.e. n is one of 1, 2, 3 and so on) increaseswithout end, (-1)" becomes closer and closer to ."Does this make sense? If so, please fill in the box. Otherwise, explain the problem![ Note that "(-1)" " means (-1) × ... × (-1), where the “(-1)" appears n times in total. ]You will have noticed that these questions are very "wordy", but somehow always have basicallythe same form. Mathematicians like to invent symbols or ways of writing which can replace longstretches of text. We can write f(x) to represent a formula which depends upon x, andlim f(x)to mean "the value, that f(x) gets ever closer to, as x gets ever closer to, but not equal to, a".The somewhat frustrating aspect of this is that we have to add "if it exists"! If it does exist,then its value is called "the limit of f(x) as x approaches a". Finally, the letters "f", "x" and"a" are just names, in the sense of Shakespeare's "A rose by any other name would smell as sweet".Now we can write question 2 above in a more compact form. If the limitlimn 00 nhas a value, then it is the value that should be put in the box for question 2.Question 4: Is this compact form (above), which clearly uses the symbol for infinity (in the

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Now we can write question 2 above in a more compact form. If the limit1limn00 nhas a value, then it is the value that should be put in the box for question 2.Question 4: Is this compact form (above), which clearly uses the symbol for infinity (in the&#34;n → 00&#34; part), consistent with what we understand to have been Aristotle's concept of infinity?Question 5: Does the limit1+nlimn-00nexist? If so, what is its value? If not, why not?Question 6: Does the limit(1+h)² – 1?limh→0exist? If so, what is its value? If not, why not?Optional Question 7 [only for bonus points]: Is it true that3 x3 xlimy→0_4x+ 5 ylimlimlimT0 4x +5 yWhy?B回回ロ凸 86%CHW有道 Question 1: The concept of infinity which is most often used in applications of mathematics toreal world problems is usually attributed to the ancient Greek philosopher Aristotle. What wasthis concept of infinity? Is it consistent with the fact that infinity is not now usually consideredto be a real number?Question 2: &#34;If n increases without end, 1/n becomes closer and closer toDoes this make sense? If so, please fill in the box. Otherwise, explain the problem!Question 3: &#34;If the positive natural number n (i.e. n is one of 1, 2, 3 and so on) increaseswithout end, (-1)&#34; becomes closer and closer to .&#34;Does this make sense? If so, please fill in the box. Otherwise, explain the problem![ Note that &#34;(-1)&#34; &#34; means (-1) × ... × (-1), where the “(-1)&#34; appears n times in total. ]You will have noticed that these questions are very &#34;wordy&#34;, but somehow always have basicallythe same form. Mathematicians like to invent symbols or ways of writing which can replace longstretches of text. We can write f(x) to represent a formula which depends upon x, andlim f(x)to mean &#34;the value, that f(x) gets ever closer to, as x gets ever closer to, but not equal to, a&#34;.The somewhat frustrating aspect of this is that we have to add &#34;if it exists&#34;! If it does exist,then its value is called &#34;the limit of f(x) as x approaches a&#34;. Finally, the letters &#34;f&#34;, &#34;x&#34; and&#34;a&#34; are just names, in the sense of Shakespeare's &#34;A rose by any other name would smell as sweet&#34;.Now we can write question 2 above in a more compact form. If the limitlimn 00 nhas a value, then it is the value that should be put in the box for question 2.Question 4: Is this compact form (above), which clearly uses the symbol for infinity (in the

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Question 5: Does the limit 1+n lim n-00 n exist? If so, what is its value? If not, why not?