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Magazine Problem 25
Approximating a Limit Graphically, use a graphing utility to graph the function and approximate the limit accurate to three decimal places. $$ \lim _{x \rightarrow 0^{+}}(x \ln x) $$
Problem 26
Sketch a graph of the function and the tangent line at the point \((1, f(1)) .\) Use the graph to approximate the slope of the tangent line. \(f(x)=\sqrt{x+3}\)
Problem 26
Approximating a Limit Graphically, use a graphing utility to graph the function and approximate the limit accurate to three decimal places. $$ \lim _{x \rightarrow 0^{+}}\left(x^{2} \ln x\right) $$
Problem 26
Evaluating a Limit at Infinity In Exercises \(9 - 28\) , find the limit (if it exists). If the limit does not exist, then explain why. Use a graphing utility to verify your result graphically. $$ \lim _ { x \rightarrow \infty } \left[ 7 + \frac { 2 x ^ { 2 } } { ( x + 3 ) ^ { 2 } } \right] $$
Problem 27
Approximating a Limit Graphically, use a graphing utility to graph the function and approximate the limit accurate to three decimal places. $$ \lim _{x \rightarrow 0}(1-x)^{2 / x} $$
Problem 27
Sketch a graph of the function and the tangent line at the point \((1, f(1)) .\) Use the graph to approximate the slope of the tangent line. \(f(x)=\frac{4}{x+1}\)
Problem 27
Evaluating a Limit at Infinity In Exercises \(9 - 28\) , find the limit (if it exists). If the limit does not exist, then explain why. Use a graphing utility to verify your result graphically. $$ \lim _ { t \rightarrow \infty } \left( \frac { 1 } { 3 t ^ { 2 } } - \frac { 5 t } { t + 2 } \right) $$
Problem 28
Sketch a graph of the function and the tangent line at the point \((1, f(1)) .\) Use the graph to approximate the slope of the tangent line. \(f(x)=\frac{3}{2-x}\)
Problem 28
Approximating a Limit Graphically, use a graphing utility to graph the function and approximate the limit accurate to three decimal places. $$ \lim _{x \rightarrow 0}(1+2 x)^{1 / x} $$
Problem 28
Evaluating a Limit at Infinity In Exercises \(9 - 28\) , find the limit (if it exists). If the limit does not exist, then explain why. Use a graphing utility to verify your result graphically. $$ \lim _ { x \rightarrow \infty } \left[ \frac { x } { 2 x + 1 } + \frac { 3 x ^ { 2 } } { ( x - 3 ) ^ { 2 } } \right] $$
