Evaluate the following limits. lim_{(x,y,z)rightarrow(0,1,0)}ln(1+y)e^{xz}

Evaluate the following limits. lim_{(x,y,z)rightarrow(0,1,0)}ln(1+y)e^{xz}

Question
Limits and continuity
asked 2020-11-08
Evaluate the following limits.
\(\lim_{(x,y,z)\rightarrow(0,1,0)}\ln(1+y)e^{xz}\)

Answers (1)

2020-11-09
Consider the following limit:
\(\lim_{(x,y,z)\rightarrow(0,1,0)}\ln(1+y)e^{xz}=\ln(1+1)e^{0\times0}\)
\(=\ln(2)e^0\)
\(=\ln(2)\times1\)
\(=\ln(2)\)
Hence, the solution is \(\lim_{(x,y,z)\rightarrow(0,1,0)}\ln(1+y)e^{xz}=\ln(2)\)
0

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