Find the limits lim_{(x,y)rightarrow(3,4)}sqrt{x^2+y^2-1}

Question
Limits and continuity
asked 2020-10-28
Find the limits
\(\lim_{(x,y)\rightarrow(3,4)}\sqrt{x^2+y^2-1}\)

Answers (1)

2020-10-29
The given expression is \(\lim_{(x,y)\rightarrow(3,4)}\sqrt{x^2+y^2-1}\)
Calculation:
\(\lim_{(x,y)\rightarrow(3,4)}\sqrt{x^2+y^2-1}=\sqrt{3^2+4^2-1}\)
\(=\sqrt{9+16-1}\)
\(=\sqrt{24}\)
\(=2\sqrt{6}\)
0

Relevant Questions

asked 2021-03-11
Evaluate the following limits.
\(\lim_{(x,y)\rightarrow(4,5)}\frac{\sqrt{x+y}-3}{x+y-9}\)
asked 2021-01-13
Evaluate the following limits.
\(\lim_{(x,y)\rightarrow(1,2)}\frac{\sqrt{y}-\sqrt{x+1}}{y-x-1}\)
asked 2021-03-07
Find the limits:
\(\lim_{(x,y)\rightarrow(0,0)}\cos\frac{x^2+y^3}{x+y+1}\)
asked 2020-10-19
Determine the limits if they exist: \(\lim_{(x,y)\rightarrow(2,4)}\frac{(x-2)^2(y-4)^2}{(x-2)^3+(y-4)^3}\)
asked 2020-10-25
Evaluate the following limits.
\(\lim_{(x,y,z)\rightarrow(1,1,1)}\frac{x-\sqrt{xz}-\sqrt{xy}+\sqrt{yz}}{x-\sqrt{xz}+\sqrt{xy}-\sqrt{yz}}\)
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 2020-11-01
Evaluate the following limits.
\(\lim_{(x,y)\rightarrow(2,-1)}(xy^8-3x^2y^3)\)
asked 2020-12-30
Evaluate the following limits. \(\lim_{(x,y)\rightarrow(e^2,4)}\ln\sqrt{xy}\)
asked 2021-03-09
Evaluate the following limits. \(\lim_{(x,y)\rightarrow(2,2)}\frac{y^2-4}{xy-2x}\)
asked 2020-12-05
Evaluate the following limits or determine that they do not exist.
\(\lim_{(x,y,z)\rightarrow(2,2,3)}\frac{x^2z-3x^2-y^2z+3y^2}{xz-3x-yz+3y}\)
...