Use the method of your choice to evaluate the following limits. lim_{(x,y)rightarrow(1,0)}frac{yln y}{x}

Use the method of your choice to evaluate the following limits. lim_{(x,y)rightarrow(1,0)}frac{yln y}{x}

Question
Limits and continuity
asked 2021-02-21
Use the method of your choice to evaluate the following limits.
\(\lim_{(x,y)\rightarrow(1,0)}\frac{y\ln y}{x}\)

Answers (1)

2021-02-22
We have to find the limit of the given function at the given point.
\(\lim_{(x,y)\rightarrow(1,0)}\frac{y\ln y}{x}\)
\(\lim_{(x,y)\rightarrow(1,0)}\frac{y\ln y}{x}\)
\(\Rightarrow\frac{0\ln0}{1}\)
now as \(\ln0=1\)
therefore
=0
i.e. \(\lim_{(x,y)\rightarrow(1,0)}\frac{y\ln y}{x}=0\)
0

Relevant Questions

asked 2021-03-06
Use the method of your choice to evaluate the following limits.
\(\lim_{(x,y)\rightarrow(2,0)}\frac{1-\cos y}{xy^2}\)
asked 2021-02-09
Use the method of your choice to evaluate the following limits.
\(\lim_{(x,y)\rightarrow(1,0)}\frac{\sin xy}{xy}\)
asked 2020-11-27
Use the method of your choice to evaluate the following limits.
\(\lim_{(x,y)\rightarrow(0,\pi/2)}\frac{1-\cos xy}{4x^2y^3}\)
asked 2021-01-02
Use the method of your choice to evaluate the following limits.
\(\lim_{(x,y)\rightarrow(0,1)}\frac{y\sin x}{x(y+1)}\)
asked 2021-01-10
Use the method of your choice to evaluate the following limits.
\(\lim_{(x,y)\rightarrow(1,1)}\frac{x^2+xy-2y^2}{2x^2-xy-y^2}\)
asked 2021-03-08
Use the method of your choice to evaluate the following limits.
\(\lim_{(x,y)\rightarrow(4,0)}x^2y\ln xy\)
asked 2021-05-12
Evaluate the following limits.
\(\lim_{(x,y,z)\rightarrow(1,1,1)}\frac{x^{2}+xy-xz-yz}{x-z}\)
asked 2021-05-30
Calculate the following limits using the factorization formula
\(x^{n}-a^{n}=1x-a21x^{n-1}+ax^{n-2}+a^{2}x^{n-3}+...+a^{n-2}x+a^{n-1}2\), where n is a positive integer a is a real number.
\(\lim_{x\rightarrow a}\frac{x^{n}-a^{n}}{x-a}\), for any positive integer n
asked 2021-05-01
Calculate the following limits using the factorization formula
\(x^{n}-a^{n}=1x-a21x^{n-1}+ax^{n-2}+a^{2}x^{n-3}+...+a^{n-2}x+a^{n-1}2\), where n is a positive integer a is a real number.
\(\lim_{x\rightarrow a}\frac{x^{5}-a^{2}}{x-a}\)
asked 2021-05-27
Calculate the following limits using the factorization formula
\(x^{n}-a^{n}=1x-a21x^{n-1}+ax^{n-2}+a^{2}x^{n-3}+...+a^{n-2}x+a^{n-1}2\), where n is a positive integer a is a real number.
\(\lim_{x\rightarrow 2}\frac{x^{5}-32}{x-2}\)
...