A. Evaluate the following limits by constructing the table values. \( \begin{array}{llll}\text { 1. } \lim _{x \rightarrow 1} 3^{x} & \text { 2. } \lim _{x \rightarrow 2} 5^{x} & \text { 3. } \lim _{x \rightarrow 4} \log x & \text { 4. } \lim _{x \rightarrow 0} \cos x\end{array} \)

To evaluate these limits, we can create a table of values approaching the limit as \( x \) nears the specified value. For \( \lim_{x \rightarrow 1} 3^{x} \): - \( x = 0.9 \) gives \( 3^{0.9} \approx 2.455 \) - \( x = 1.0 \) gives \( 3^{1.0} = 3 \) - \( x = 1.1 \) gives \( 3^{1.1} \approx 3.245 \) For \( \lim_{x \rightarrow 2} 5^{x} \): - \( x = 1.9 \) gives \( 5^{1.9} \approx 4.273 \) - \( x = 2.0 \) gives \( 5^{2.0} = 25 \) - \( x = 2.1 \) gives \( 5^{2.1} \approx 25.875 \) For \( \lim_{x \rightarrow 4} \log x \): - \( x = 3.9 \) gives \( \log 3.9 \approx 0.591 \) - \( x = 4.0 \) gives \( \log 4.0 \approx 1.386 \) - \( x = 4.1 \) gives \( \log 4.1 \approx 1.410 \) For \( \lim_{x \rightarrow 0} \cos x \): - \( x = -0.1 \) gives \( \cos(-0.1) \approx 0.995 \) - \( x = 0.0 \) gives \( \cos(0.0) = 1 \) - \( x = 0.1 \) gives \( \cos(0.1) \approx 0.995 \) Thus, the evaluated limits are: 1. \( \lim_{x \rightarrow 1} 3^{x} = 3 \) 2. \( \lim_{x \rightarrow 2} 5^{x} = 25 \) 3. \( \lim_{x \rightarrow 4} \log x = \log 4 \approx 1.386 \) 4. \( \lim_{x \rightarrow 0} \cos x = 1 \)