Question

CAN YOU PLEASE SOLVE QUESTION 3 PART C ? THANKS IN ADVANCE.

l'Hospitalizatióll Note: Remember always to applicable ways to indicate whether you are using l'Hospital's Rule and (if you ar 1. Do not evaluate any of the following limits lim, In(x) o ez lim+1 -W+In(2) sin(x) Inn e -z linz → 1 (z-1) ln(x) lim (Indicate type) (a) Which of the above limits are in indeterminate form? (b) Which are in a correct form for using I'Hospital's Rule? 2. Let's examine "O"... (a) John says that 00 0, because 0,= 0 for any z. Convince John that he is wron evaluating lim,t,20, which should equal 00 if 00 is a number. by evaluating lime-+00°, which should equal 0° if 00 is a number. evaluating In(L)-lim,→0+ In (r). This will require l'Hospital's rule-what does (b) Tracey says that 01, because z 1 for any s. Convince Tracey that she is wro (c) Pattries to compromise between John and Tracey by setting L = limx-0+ tx and discover? 3. In this problem we will explore why "1o0" is an indeterminate form. (a) Prove that (1+)-1 (b) Prove that zlin (1+x) = e (c) Prove that lim AlddeiMnAte ndeferm In c 4. Evaluate the following limits: (a) lim-凹, where n is any positive integer. ェ e (b) lim where n is any positive integer Hint: It might help to first consider lim, limlim et Unless you really want to and have finished the rest of the worksheet. This doesn't prove that Tracey is correct, by the way- because we have found two limits of the forn different values, we have demonstrated that "o is an indeterminate form. 53