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

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

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 $$\lim_{(x,y,z)\rightarrow(0,1,0)}\ln(1+y)e^{xz}=\ln(2)$$

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