Chapter 3
Calculus for Biology and Medicine · 168 exercises
Problem 42
In Problems \(29-48\), find the limits. $$ \lim _{x \rightarrow 0} \frac{e^{-x}-e^{x}}{e^{-x}+1} $$
3 step solution
Problem 43
In Problems \(37-54\), use the limit laws to evaluate each limit. $$ \lim _{x \rightarrow-3} \frac{x^{3}-20}{x+1} $$
2 step solution
Problem 43
In Problems \(29-48\), find the limits. $$ \lim _{x \rightarrow-2} \frac{1}{\sqrt{5 x^{2}-4}} $$
3 step solution
Problem 44
In Problems \(37-54\), use the limit laws to evaluate each limit. $$ \lim _{x \rightarrow 1} \frac{x^{3}-1}{x+2} $$
2 step solution
Problem 44
In Problems \(29-48\), find the limits. $$ \lim _{x \rightarrow 1} \frac{1}{\sqrt{3-2 x^{2}}} $$
2 step solution
Problem 45
In Problems \(37-54\), use the limit laws to evaluate each limit. $$ \lim _{x \rightarrow 3} \frac{3 x^{2}+1}{2 x-3} $$
4 step solution
Problem 45
In Problems \(29-48\), find the limits. $$ \lim _{x \rightarrow 0} \frac{\sqrt{x^{2}+9}-3}{x^{2}} $$
5 step solution
Problem 46
In Problems \(37-54\), use the limit laws to evaluate each limit. $$ \lim _{x \rightarrow-2} \frac{1+x}{1-x} $$
5 step solution
Problem 46
In Problems \(29-48\), find the limits. $$ \lim _{x \rightarrow 0} \frac{5-\sqrt{25+x^{2}}}{2 x^{2}} $$
5 step solution
Problem 47
In Problems \(37-54\), use the limit laws to evaluate each limit. $$ \lim _{x \rightarrow 1} \frac{1-x^{2}}{1-x} $$
4 step solution
Problem 47
In Problems \(29-48\), find the limits. $$ \lim _{x \rightarrow 0} \ln (1-x) $$
3 step solution
Problem 48
In Problems \(37-54\), use the limit laws to evaluate each limit. $$ \lim _{u \rightarrow 3} \frac{9-u^{2}}{3-u} $$
5 step solution
Problem 48
In Problems \(29-48\), find the limits. $$ \lim _{x \rightarrow 1} \ln \left[e^{x} \cos (x-1)\right] $$
5 step solution
Problem 49
In Problems \(37-54\), use the limit laws to evaluate each limit. $$ \lim _{x \rightarrow 3} \frac{x^{2}-2 x-3}{x-3} $$
5 step solution
Problem 50
In Problems \(37-54\), use the limit laws to evaluate each limit. $$ \lim _{x \rightarrow 1} \frac{(x-1)^{2}}{x^{2}-1} $$
5 step solution
Problem 51
In Problems \(37-54\), use the limit laws to evaluate each limit. $$ \lim _{x \rightarrow 2} \frac{2-x}{x^{2}-4} $$
4 step solution
Problem 52
In Problems \(37-54\), use the limit laws to evaluate each limit. $$ \lim _{x \rightarrow-4} \frac{x+4}{16-x^{2}} $$
5 step solution
Problem 54
In Problems \(37-54\), use the limit laws to evaluate each limit. $$ \lim _{x \rightarrow 1 / 2} \frac{1-x-2 x^{2}}{1-2 x} $$
5 step solution