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Evaluate the following limit. Use IHopital s Rule when it is convenient and applicable_T1xx-0lim xlIx = (Type an exact answer:) X-+0`...

Question

Evaluate the following limit. Use IHopital s Rule when it is convenient and applicable_T1xx-0lim xlIx = (Type an exact answer:) X-+0`

Evaluate the following limit. Use IHopital s Rule when it is convenient and applicable_ T1x x-0 lim xlIx = (Type an exact answer:) X-+0`



Answers

Limits Evaluate the following limits. Use l'Hópital's Rule when it is comvenient and applicable. $$\lim _{x \rightarrow 0^{+}} x^{2 x}$$

Hello to our weapons. Our problem about 63 here. The giver we heard Evaluate. Believe it extends doing Vendee exit, square minus square or both. Thank first to for plus 16 square. This can be bitterness limited extends to infinity minus 16. Thanks. A square different by It's a square plus fruit gulf exist. Therefore blessed 16 paperclip. Okay, so you bet. If you're playing for difference between 13. 30 by activities and entertainment for so play Hill Hospital. So we got living extents to infinity minus 60. Next square is like I wanna go to a lot of it. They really exclaimed, excluding going by in a 16. Okay, You know, I'm just glad. So here we go. More plus square. It's just awful to be counselor 16 but pay for Quit. Okay. They this in the square and visit the square. Can we can't, uh, no place to make your credit limit extends to infinity in 30 minus $16. Why? Bless square or no barn plus 16 by included one by 30 0 right now succeeded by learn. Plus, we're told our pleasure, which is equal to minus 60. But my guess. Mark Portico minus eight. Thank you.

Hello. So in this given So in this given question, we have to find a value off this limit function. Okay. This'll is very simple. What we have to do is where do you live? Like this function? We can write it like limit extends to zero A to the power X log off, then hyperbolic x from Or we can write it us A. To the power limit extends to zero. Log off, then Hyperbolic ax divided by X so fast off all we will calculate this function. Okay, so that Z one second soul Uh, yeah. So we'll calculate this first function. So when we put the value off access jiggle, we get bigger upon So it is in the farm off upon we can play develop it a little on this function when we airplay. Let's suppose Mrs l So it becomes limit. X dash Does you know when we differentiate the numerator and denominator, it becomes sick. Hyperbolic squared X divided by 10 hyperbolic X divided by minus off one upon access square. Okay. When we substitute the sigh Keiper bolic access one upon course Hyperbolic x so it becomes minus self limit exchange to judo excess squared upon because hyperbolic squared X stan Hyperbolic x. Okay, then the next step is to simplify this so it becomes minus off. Let me the extent to judo access credit upon Sign it sine hyperbolic x and cause hyperbolic x. Okay, so it becomes when we again simplify this it becomes minus off toe limit extends to zero excess square upon sine hyperbolic to works here. We didn't do anything here. We just have multiplied your matter and the nominal by two. So this denominator will become sine hyperbolic. Two x Okay. So in the next step we have to apply again. I'll help it a little because when we put the value off access to you here it becomes in the form of Judah upon judo. So we have to apply this school. When we apply this rule, it becomes minus to limit extends to zero to X upon to cause hyperbolic to works which is a close to minus two. Now we can put the limit when they put access to you know, we get Jesus up on cause hyperbolic judo. So cause hyperbolic Gero is request to one so minus two into zero upon one which is request. Oh, jeez. Oh, Now, the last step is to put the value off this function. You never in a first in our first funds. In a given question, this question she so many substitute the value off. This is we get into the pejeta, which is a cost to one. So the given for for the final solution for the given question is one.

In this question you have to find the limit of dysfunction using hospitals, food in a according to this rule. Uh If we have given a function of type limit extends to a and topics by the opec, then we can replace it with a limit of extends to a and a dash of eggs. Where do you lash out Where evidential facts and judicial picks are the derivative of politics and geography. This rule we can apply only, we get an indeterminate form Of zero x 0 Plus- Infinity. Where plus minus infinity on substituting the value of X in the given function. Like in this function if we substitute eggs as -1, we get an indeterminate form of zero by zero. Therefore, according to a hospital school we have to find the derivative of F. For facts which is expe our food plus two eggs plus one and G. O. Fix is X powerful minus two. A. It's 35 -2 X -1. Therefore All applying hospital school limit of extends to -1 will be and best of X which is four X. Q. Let's two by Geo Judah shop X. That is five x. Power food minus two Which will be equal to also shooting excess -1. Pour into -1 you first to. Yeah. Where did by plane -24 -2. Therefore limit of the function will be -4 Plus two. Buddy 5- which will be equal to -2 x three. This is the limiter dysfunction. Thank you.

In this question we have to find the limit of dysfunction. Using a hospital. Through. According to this rule, we get an indeterminate form of 0x0. Are last minus infinity by plus minus infinity on substituting the value of X in the given function. Then we can apply the hospitals. So in this question All substituting -1 in the function, We get an indeterminate form of 0-0. So water school says that if the given function is uptight limit extends to aid it's all fixed. But your picks then we can transform it to limit extends to age and additional fixed. What is the additional thing? Very special fixing? Judicial Brexit derivative derivative of That's perfect. And judicial. NGO. Now that's all this question. Oh. Uh huh. Are they will be -1? Full flexibility for four plus 2 weeks last one. But Yes actually explored 5 -2. It my next blood. No, I'm not playing a hospital screwed limit extends to my next one. We need to find evidential fix. The test. Did you want to have sex? Mhm. Or X. Q. Last two. Bye five. X. Power tools minus two five X 4 for -2. Will be your judicial tax knowledge. Substitute the value of X. In the function. It will give us the limit. 5 -1. Power. 4 -2. No Will be -4-plus 2. Five minutes. To Limit will be -2. But thank you.


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