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In this lesson, we will learn how to find the limit of a function in more than one variable as we approach a point in the domain of the function.

Q1:

Evaluate if it exists.

Q2:

Evaluate the limit l i m s i n ( π₯ , π¦ ) β ( 0 , 0 ) 2 2 4 4 π¦ π₯ π₯ + π¦ , if it exists.

Q3:

Evaluate the limit l i m c o s ( π₯ , π¦ ) β ( 0 , 0 ) 2 2 οΉ π₯ + π¦ ο ο½ 1 π₯ π¦ ο , if it exists.

Q4:

Evaluate l i m ( π₯ , π¦ ) β ( 0 , 0 ) 3 3 2 2 π₯ β π¦ π₯ + π₯ π¦ + π¦ , if it exists.

Q5:

Evaluate the limit l i m ( π₯ , π¦ ) β ( 1 , 0 ) 2 2 π₯ π¦ β π¦ ( π₯ β 1 ) + π¦ , if it exists.

Q6:

Evaluate l i m ( π₯ , π¦ ) β ( 0 , 0 ) 2 2 2 π₯ π¦ π₯ + π¦ , if it exists.

Q7:

Evaluate l i m c o s ( π₯ , π¦ ) β ( 0 , 0 ) ο½ 1 π₯ π¦ ο , if it exists.

Q8:

Evaluate the limit l i m ( π₯ , π¦ ) β ( 0 , 0 ) 2 2 2 2 π₯ + π¦ β π₯ + π¦ + 1 β 1 , if it exists.

Q9:

Evaluate l i m ( π₯ , π¦ ) β ( 1 , β 1 ) 2 2 π₯ β 2 π₯ π¦ + π¦ π₯ β π¦ , if it exists.

Q10:

Evaluate the limit l i m ( π₯ , π¦ ) β ( 0 , 0 ) 2 2 4 π₯ π¦ π₯ + π¦ , if it exists.

Q11:

Evaluate the limit l i m ( π₯ , π¦ ) β ( 0 , 0 ) 4 2 8 π₯ π¦ π₯ + π¦ , if it exists.

Q12:

Evaluate the limit l i m s i n ( ο ο ο ) β ( ο¦ ο ο¦ ) οͺ ο¨ ο¨ π¦ π₯ π¦ π₯ + π¦ , if it exists.

Q13:

Evaluate the limit l i m ( ο ο ο ) β ( ο¦ ο ο¦ ) ο¨ ο¨ ο¨ ο¨ π₯ β π¦ π₯ + π¦ , if it exists.

Q14:

Evaluate l i m ( ο ο ο ) β ( ο¦ ο ο¦ ) ο¨ ο¨ ο¨ π₯ π¦ π₯ + π¦ , if it exists.

Q15:

Evaluate l i m ( ο ο ο ) β ( ο¦ ο ο¦ ) οͺ ο¨ ο¨ ο¨ π₯ β 4 π¦ π₯ + 2 π¦ , if it exists.

Q16:

Evaluate l i m ( π₯ , π¦ ) β ( 3 , 2 ) 2 3 2 οΉ π₯ π¦ β 4 π¦ ο , if it exists.

Q17:

Evaluate l i m ( π₯ , π¦ ) β ( 0 , 0 ) 4 4 4 π₯ π¦ π₯ + π¦ , if it exists.

Q18:

Evaluate l i m ( π₯ , π¦ , π§ ) β ( 0 , 0 , 0 ) 2 2 2 2 2 2 π₯ π¦ π§ π₯ + π¦ + π§ , if it exists.

Q19:

Evaluate l i m c o s ( π₯ , π¦ ) β ( 0 , 0 ) 4 2 4 4 5 π¦ π₯ π₯ + π¦ if it exists.

Q20:

Evaluate l i m t a n ( π₯ , π¦ , π§ ) β ( π , 0 , ) π¦ 1 3 2 π π₯ π§ , if it exists.

Q21:

Evaluate the limit, if it exists.

Q22:

Evaluate l i m ( π₯ , π¦ ) β ( 0 , 0 ) π₯ π¦ π , if it exists.

Q23:

Evaluate l i m s i n ( π₯ , π¦ ) β ( π , ) π 2 π¦ ( π₯ β π¦ ) , if it exists.

Q24:

Q25:

Evaluate the limit l i m ( ο ο ο ) β ( ο§ ο ο± ο¨ ) β ο¨ ο ο± ο π , if it exists.

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