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lim xsin(1/x) as x goes to 0

In this video, I explained the 4 common methods of taking limits. I also solved the limit problem showing that only one of the 4 methods was relevant. The other 3 just didn't work.

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Integrate x^-x dx
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Integrate x^-x dx

Limit of absolute value functions [ lim |x^3 - x|/(x^3 - |x|) as x goes  to  0 ]
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Limit of absolute value functions [ lim |x^3 - x|/(x^3 - |x|) as x goes to 0 ]

Integrate 1/(1+x^3)
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Integrate 1/(1+x^3)

The Limit (do not use L'Hospital rule)
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The Limit (do not use L'Hospital rule)

What is 0 to the power of 0?
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What is 0 to the power of 0?

Proofs: Lim sinx/x =1 and lim [cosx -1] /x =0 as x goes to zero from geometry
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Proofs: Lim sinx/x =1 and lim [cosx -1] /x =0 as x goes to zero from geometry

What Lies Between a Function and Its Derivative? | Fractional Calculus
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What Lies Between a Function and Its Derivative? | Fractional Calculus

The most important limit in Calculus // Geometric Proof & Applications
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The most important limit in Calculus // Geometric Proof & Applications

The Calculus Idea I Wish Had Been Explained First
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The Calculus Idea I Wish Had Been Explained First

Proof of a Limit Value Using Epsilon and Delta
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Proof of a Limit Value Using Epsilon and Delta

The essence of calculus
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The essence of calculus

Innocent looking, but ????
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Innocent looking, but ????

Why The Limit Does Not Exist
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Why The Limit Does Not Exist

The Derivative - The MOST Important Concept in Calculus
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The Derivative - The MOST Important Concept in Calculus

How To Find The Limit At Infinity
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How To Find The Limit At Infinity

Taylor series | Chapter 11, Essence of calculus
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Taylor series | Chapter 11, Essence of calculus

Complex Integration and Finding Zeros of the Zeta Function
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Complex Integration and Finding Zeros of the Zeta Function

Best Explanation of Gradient, Divergence and Curl
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Best Explanation of Gradient, Divergence and Curl

When CAN'T Math Be Generalized? | The Limits of Analytic Continuation
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When CAN'T Math Be Generalized? | The Limits of Analytic Continuation

Lambert W Function
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Lambert W Function

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