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I +1 2 11. (10-points) lim € +0+ x x3)...

Question

I +1 2 11. (10-points) lim € +0+ x x3)

I +1 2 11. (10-points) lim € +0+ x x3)



Answers

\lim _{x \rightarrow-2} \frac{x^{2}+5 x+6}{x+2} \text { \{Ans. 1\} }

In the solution we have to find the limiter. This function limit accidents to seal oh one plus 2. Act To the post seven -1 blows three eggs to deport. Why upon X. So here we know that by normal threes which is one plus act to devote E. Equal to one blues. Next time E blues eight times E. Negative one upon pictorial too. Times access choir close ranks on. So now we apply here limit accidents to zero all one blues seven kinds through A plus 17 6 equal to 42 upon to equal to 21 times two X. Squared and so on negative one blood five times 3 x. Positive 10 times three X. Squared and so on upon X. So here we combine like terms. So here we get limit Extends to 00.1 negative unequal to zero. And here For the next -15 x. So you can write like that 15 x. Which is negative positive 14 X. Equal to negative act negative 66 square and so on Upon X. So here we like this year which is negative X. So here we get limit accidents to zero. All negative X. Time one first six times X. And so on on. Act. So here actually begins allowed. And here you can see that man reports limit. So here we only get post from which is one and all the terms will be zero. So here we get negative one time positive one equal to 91. So here it is the limit of dysfunction. It is so it is my answer

In description we have to find the limited operational functions so here given limit extends to two of XQ was three times access choir -9 negative too upon Excuse Night two x night six so in the execution first of all we find the factor of numerator and denominator so here you can see that the factor of excuse Close three x Squire -9 X -2 equal to xnegative too. Times access quiet was five plus one and The factor of execute negative X -6 equal to X -2 times X squared plus two eggs plus three so now we put here so we get limit accidents to to of X -2 times access choir plus five X plus one upon X -2 times X squared plus two X plus three. So now here you can see that X # two will be cancelled out. So here we get limit Extends to two of access choir close five x plus one upon access square close to eggs was three so now here we puts limit accidents to two So here we get To do the power to plus five times 2 plus one upon 2 to the power to Plus two times 2 close three so here we get foreclosed 10 plus one upon four plus four plus three equal 15 upon 11 so here the limit of rational function which is 15 upon 11 which is worth

Okay, so we're actually find a limited the falling. So let's use our quotient role. So we're gonna take the limits as X approaches to of our numerator over the limit. There's expertise to of our denominator that's is equal to two times two plus five over 11 when it's 2 to 3, and that's four plus 5/11 minus eight. That's 9/11 minutes. Age, which is equal to three and 9/3, is a cultivated.

In this situation we have to find the limit of defined an article function and here which is limited Extends to one all three times x squared plus four times X plus five. So now you can write like that limit Extends to one off three X Squire plus limit Extends to one of four X. Less limit extends to one of five. So now here Limit accidents to one of three times access square. So now here we get three times 1 to the power to in the second term limit accidents to one of four x. So now here we get four times one. So now we're here and here you can see that limit accidents to one all fives and fights a constant so we can put here five. So now Here we get three plus four plus five. That is the value of limit accidents to one of three times X squared plus four X plus five, which is 12. So it is over. Final answer.


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