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Question 1: (8 marks) Comeute the iollowing limits, ifpossible on the type of limit If a limit For each of them; SHOW YOUR is equal t0 c or ~0 , mention it, WORK,...

Question

Question 1: (8 marks) Comeute the iollowing limits, ifpossible on the type of limit If a limit For each of them; SHOW YOUR is equal t0 c or ~0 , mention it, WORK, arguing marks) Jim 6x -7x+1b) (5 marks) lim (Hint: After expression as having ratio of two found the form Nole: The next page polynomials. of the limit, was rewrite this left blank to let you ore space (0 write your answer.

Question 1: (8 marks) Comeute the iollowing limits, ifpossible on the type of limit If a limit For each of them; SHOW YOUR is equal t0 c or ~0 , mention it, WORK, arguing marks) Jim 6x -7x+1 b) (5 marks) lim (Hint: After expression as having ratio of two found the form Nole: The next page polynomials. of the limit, was rewrite this left blank to let you ore space (0 write your answer.



Answers

$1-4$ Given that
$$\begin{array}{c}{\lim _{x \rightarrow a} f(x)=0 \quad \lim _{x \rightarrow a} g(x)=0 \quad \lim _{x \rightarrow a} h(x)=1} \\ {\lim _{x \rightarrow a} p(x)=\infty \quad \lim _{x \rightarrow a} q(x)=\infty}\end{array}$$
which of the following limits are indeterminate forms? For
those that are not an indeterminate form, evaluate the limit where
possible.
$$\begin{array}{l}{\text { (a) } \lim _{x \rightarrow a}[f(x)-p(x)]} \\ {\text { (c) } \lim _{x \rightarrow a}[p(x)+q(x)]}\end{array} \quad \text { (b) } \lim _{x \rightarrow a}[p(x)-q(x)]$$

Yeah, So in this question, we have been given these Carlos on. We have to find the middle exchange toe for affects My geo effects extends to F off X records. Iran G off X is also called to zero, So this will be for 20 by zero, which is an indeterminate form. Then the next limit exchange to F off X Y P off X would be equal to zero divided by infinity, which will be equal to zero. So this is not an indeterminant form. Similarly, limit exchange to edge off X by P off X will be equal to one diverted by infinity, which would also equal to zero. So this is also not any indeterminate from now. Limit extends to the F d off X by a for affects will be quarto infinity divided by zero. Here, if we find out the right hand limit at extends to zero plus we'll get plus infinity and the left can limit exchange 20 minus will get minus infinity since both limits are not equal. Therefore, the limit might not exist for this For the last one limit extends to happy off X y que off X will be equal to infinity by infinity, which is indeterminate from

Our goal for this particular problem is to determine which of the following have indeterminate forms. So the first one is going to be F of x minus P of x, which will be zero minus infinity, and that's just gonna end up giving us a negative infinity. Then we'll have um p of X times kovacs, so it's going to be infinity, find infinity uh P of X times Q beck. So infinity times infinity is going to be infinity. So that's not an indeterminate form. And then lastly, we're going to have P of X plus Q of X, which is infinity plus infinity. And that is also not going to be an indeterminate form, that one would be infinity. So that's our final answer. Yeah. Mhm.

Our goal is to determine which of the following are indeterminate forms. So we're going to have F of X times P of X. So really what that's going to look like is zero times infinity and that's going to be indeterminant. Then we have a choice of X times P of X, Which is going to be one times infinity. And even though the show is undefined, it really is actually equal to infinity. So that's not going to be undefined. It's undefined in the sense that infinity can't really be defined. But um and then lastly, we have P of X times Q of X. That's infinity times infinity. Okay. And we know that that is just going to be infinity. So that one is not indeterminant form either. And that one will be our final answer. There's a list of indeterminate forms and we're going to need to know them when we're applying reptiles rule.

We have to find that indeterminant forms of the given limits. So party here you go in limit extends to a F Xbox LTD. Extends to a do FX P X. Okay, so limit extends to a is given zero, and limited extends to a PX in 20. So it is in the it is in the form of zero into infinity. Okay, so we can write it like this. Limit like limit extends to a Yeah, limit extends to a effects of phone. One of one PX to limit extends to fx zero and limit exchange to a burn upon PS will be at 20 So it will be zero comma 000 form or yes, we can also write this. We can also write it like this like PX upon one of on FX. So it will be in plenty of one in 24. So this party is indefinite. Indeterminate form, indeterminate noodle made from the part of me is given. Yeah, yeah, and the part of it given limit extends to H XP. X limit extends to a Yeah. Okay. Head jokes P x. So we can I d like this limit extends to attacks is given one. It is given one and limitation to a PFS in pretty. So it will be in a pretty in the Parsi and the party is given limit extends to a PS QX limit extends to a P X ups and P X limited exchange to a PX has given in 20 and the taxes also in painting. So so it will be in printing, I hope your initial and thank you. Yeah.


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