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Chapter 4: Problem 40
Evaluate the following limits. $$\lim _{x \rightarrow \infty} \frac{e^{3 x}}{3 e^{3 x}+5}$$
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Given the following velocity functions of an object moving along a line, find the position function with the given initial position. Then graph both the velocity and position functions. $$v(t)=2 \cos t ; s(0)=0$$
The ranking of growth rates given in the text applies for \(x \rightarrow
\infty .\) However, these rates may not be evident for small values of \(x .\)
For example, an exponential grows faster than any power of \(x .\) However, for
\(1
Use analytical methods to evaluate the following limits. $$\lim _{x \rightarrow \infty} \frac{\log _{2} x}{\log _{3} x}$$
Evaluate the following limits in two different ways: One of the ways should use l' H么pital's Rule. $$\lim _{x \rightarrow \infty} \frac{2 x^{3}-x^{2}+1}{5 x^{3}+2 x}$$
Differentials Consider the following functions and express the relationship between a small change in \(x\) and the corresponding change in \(y\) in the form \(d y=f^{\prime}(x) d x\) $$f(x)=e^{2 x}$$
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