Let . Calculate š

**Solution**

—>Ā

we know thatĀ

SoĀ

—>Ā

–> Ā

*** By Taylor series

ThereforeĀ

Let . Calculate š

**Solution**

—>Ā

we know thatĀ

SoĀ

—>Ā

–> Ā

*** By Taylor series

ThereforeĀ

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Anyone can do it?? then compare with my answer =š I don’t want to post itš I’m not sure my solution is right or wrongš thank youš My answer that I got is completely wrongš

We givenĀ andĀ

find the solution ofĀ š

Here is the link to see the answer:

Answer here

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Find theĀ ?š

**Solution**

Use The L’Hopital’s Rule forĀ

Plugging x=1 then we getĀ

ThereforeĀ

Thank youš

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Compute ?š

**Solution**

SinceĀ

We multiply the numerator and denominator byĀ and use the fact thatĀ Therefore:

**Another solution, usingĀ L’Hopital’s rule, is possible:Ā

Thank youš

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1. Choose any three-digit number (where the units and hundreds digits are not the same).

We will do it with you here by arbitrarily selecting 825.

2. Reverse the digits of this number you have selected.

We will continue here by reversing the digits of 825 to get 528.

3. Subtract the two numbers (naturally, the larger minus the smaller).

Our calculated difference is 825 ā 528 = 297.

4. Once again, reverse the digits of this difference.

Reversing the digits of 297 we get the number 792.

5. Now, add your last two numbers.

We then add the last two numbers to get 297 + 792 = 1089.

Their result should be the sameā as ours even though their starting numberswere different from ours.

They will probably be astonished that regardless of which numbers theyselected at the beginning, they got the same result as we did, 1,089.How does this happen? Is this a āfreak propertyā of this number? Did wedo something devious in our calculations?

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Compute :DĀ š

**Solution**

Using the fact thatĀ , we evaluate the integral as follows:

Noticing that the derivative ofĀ isĀ , it follows that the integral evaluates toĀ

Evaluate this fromĀ toĀ we obtain the answerĀ š

Remember to change from x to uš

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The differentiable function : satisfied and

Find as a function of .

**Solution**

SubstitutionĀ

thenĀ

So we getĀ

since we know thatĀ then we getĀ

Therefore

š Thank you Pablo for comment about š

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