 Recent questions in Rational functions Stefan Hendricks 2021-12-20 Answered

2021-12-13

Perform the indicated operation h(n) = 4n-4 g(n) = n^2+3n find (h*g)(2) jack89515lg 2021-12-01 Answered

True or False. Every rational function has at least one vertical asymptote. Line 2021-10-26 Answered

The rate of return. Given information: $$\begin{array}{|c|c|} \hline Year & Cash\ Flow&IRR@39\%&Present\ Value \\ \hline 0 & -200&0&-200\\ \hline 1&350&0.719&251.65\\ \hline 2&-100&0.517&-51.70\\ \hline \end{array}$$ As PV at $$\displaystyle{39}\%$$ is zero. So, the rate of return is $$\displaystyle{39}\%$$. PV Value at $$\displaystyle{39}\%$$ is calculated using the table. texelaare 2021-09-25 Answered

Use substitution to convert the integrals to integrals of rational functions. Then use partial fractions to evaluate the integrals. $$\displaystyle\int{\frac{{{\cos{{x}}}}}{{{\sin{{x}}}{\left({1}-{\sin{{x}}}\right)}}}}{\left.{d}{x}\right.}$$ illusiia 2021-09-25 Answered

The process by which we determine limits of rational functions applies equally well to ratios containing noninteger or negative powers of x: Divide numerator and denominator by the highest power of x in the denominator and proceed from there. Find the limits. $$\displaystyle\lim_{{x}→∞}\frac{{{x}−{3}}}{{√{4}{x}^{{2}}+{25}}}$$ vazelinahS 2021-09-24 Answered

Determine $$\displaystyle\lim_{{{x}\rightarrow\infty}}{f{{\left({x}\right)}}}$$ and $$\displaystyle\lim_{{{x}\rightarrow-\infty}}{f{{\left({x}\right)}}}$$ for the following rational functions. Then give the horizontal asymptote of f (if any). $$\displaystyle{f{{\left({x}\right)}}}={\frac{{-{x}^{{{3}}}+{1}}}{{{2}{x}+{8}}}}$$ Tahmid Knox 2021-09-24 Answered

For the following exercises, find the domain of the rational functions. $$\displaystyle{f{{\left({x}\right)}}}={\frac{{{x}^{{{2}}}+{4}}}{{{x}^{{{2}}}-{2}{x}-{8}}}}$$ banganX 2021-09-23 Answered

Investigate asymptotes of rational functions. Copy and complete the table. Determine the horizontal asymptote of each function algebraically. Function Horizontal Asymptote $$\displaystyle{f{{\left({x}\right)}}}=\frac{{{x}^{{2}}-{5}{x}{4}}}{{{x}^{{3}}+{2}}}$$ $$\displaystyle{h}{\left({x}\right)}=\frac{{{x}^{{3}}-{3}{x}^{{2}}+{4}{x}-{12}}}{{{x}^{{4}}-{4}}}$$ $$\displaystyle{g{{\left({x}\right)}}}=\frac{{{x}^{{4}}-{1}}}{{{x}^{{5}}+{3}}}$$ Sinead Mcgee 2021-09-22 Answered

(a) rewrite the sum as a rational function S(n), (b) use S(n) to complete the table, and (c) find $$\displaystyle\lim_{{n}→∞}{S}{\left({n}\right)}$$ $$S(n)=100, 101, 102, 103, 104$$ $$\displaystyle{\sum_{{{i}={1}}}^{{n}}}{\frac{{{3}}}{{{n}^{{{3}}}}}}{\left({1}+{i}^{{{2}}}\right)}$$ Tazmin Horton 2021-09-21 Answered

Use substitution to convert the integrals to integrals of rational functions. Then use partial fractions to evaluate the integrals. $$\displaystyle\int{\frac{{{1}+\epsilon^{{{x}}}}}{{{1}-\epsilon^{{{x}}}}}}{\left.{d}{x}\right.}$$ Cheyanne Leigh 2021-09-19 Answered

Use substitution to convert the integrals to integrals of rational functions. Then use partial fractions to evaluate the integrals. $$\int \frac{dx}{\sqrt{x}+\sqrt{x}}$$ iohanetc 2021-09-17 Answered

Determine $$\displaystyle\lim_{{{x}\rightarrow\infty}}{f{{\left({x}\right)}}}$$ and $$\displaystyle\lim_{{{x}\rightarrow-\infty}}{f{{\left({x}\right)}}}\rbrace$$ for the following rational functions. Then give the horizontal asymptote of f (if any). $$\displaystyle{f{{\left({x}\right)}}}={\frac{{{x}^{4}+{7}}}{{{x}{5}+{x}^{{{2}}}-{x}}}}−{x}$$ smileycellist2 2021-09-17 Answered

Graph each of the following rational functions. State the equations of the asymptotes. a) $$\displaystyle{j}{\left({x}\right)}=-{\frac{{{6}}}{{{x}+{4}}}}+{7}$$ b) $$\displaystyle{k}{\left({x}\right)}={\frac{{{x}+{6}}}{{{2}{x}-{4}}}}$$ Caelan 2021-09-17 Answered

Consider the following sets of rational functions. $$\displaystyle{a}{f{{\left({x}\right)}}}={\frac{{{a}}}{{{x}}}}$$ for a={−2,−1,−0.5,0.5,2,4}, $$\displaystyle{h}{\left({x}-{c}\right)}={\frac{{{1}}}{{{x}-{c}}}}$$​ for c=[−4,−2,−0.5,0.5,2,4], h(x−c)=1x−c for c=[−4,−2,−0.5,0.5,2,4], g(bx)=1bx for b={−2,−1,−0.5,0.5,2,4} for b={−2,−1,−0.5,0.5,2,4}, $$\displaystyle{k}{\left({x}\right)}+{d}={\frac{{{1}}}{{{x}}}}+{d}$$ for d={−4,−2,−0.5,0.5,2,4} for d={−4,−2,−0.5,0.5,2,4}. a. Graph each set of functions on a graphing calculator. jernplate8 2021-09-16 Answered

$$\displaystyle\lim_{{{x}\rightarrow-\infty}}{\frac{{\sqrt{{{3}}}{\left\lbrace{x}\right\rbrace}-\sqrt{{{5}}}{\left\lbrace{x}\right\rbrace}}}{{\sqrt{{{3}}}{\left\lbrace{x}\right\rbrace}+\sqrt{{{5}}}{\left\lbrace{x}\right\rbrace}}}}$$ arenceabigns 2021-09-15 Answered

Let F be the field of rational functions described in the Example. (a) Show that the ordering given there satisfies the order axioms O1, O2, and O3. (b) Write the following polynomials in order of increasing size: $$\displaystyle{x}^{{{2}}},−{x}^{{{3}}},{5},{x}+{2},{3}−{x}$$. (c) Write the following functions in order of increasing size: $$\displaystyle{\frac{{{x}^{{{2}}}+{2}}}{{{x}-{1}}}},{\frac{{{x}^{{{2}}}-{2}}}{{{x}+{1}}}},{\frac{{{x}+{1}}}{{{x}^{{{2}}}-{2}}}},{\frac{{{x}+{2}}}{{{x}^{{{2}}}-{1}}}}$$. CMIIh 2021-09-15 Answered

Consider the following sets of rational functions. $$\displaystyle{a}{f{{\left({x}\right)}}}={\frac{{{a}}}{{{x}}}}$$ for a={−2,−1,−0.5,0.5,2,4}, $$\displaystyle{h}{\left({x}-{c}\right)}={\frac{{{1}}}{{{x}-{c}}}}$$​ for c=[−4,−2,−0.5,0.5,2,4], h(x−c)=1x−c for c=[−4,−2,−0.5,0.5,2,4], g(bx)=1bx for b={−2,−1,−0.5,0.5,2,4} for b={−2,−1,−0.5,0.5,2,4}, $$\displaystyle{k}{\left({x}\right)}+{d}={\frac{{{1}}}{{{x}}}}+{d}$$ for d={−4,−2,−0.5,0.5,2,4} for d={−4,−2,−0.5,0.5,2,4}. c. Choose two functions from any set. Find the slope between consecutive points on the graphs. aortiH 2021-09-14 Answered

The process by which we determine limits of rational functions applies equally well to ratios containing noninteger or negative powers of x: Divide numerator and denominator by the highest power of x in the denominator and proceed from there. Find the limits. $$\displaystyle\lim_{{{x}\rightarrow-\infty}}\sqrt{{{\frac{{{x}^{{{2}}}-{5}{x}}}{{{x}^{{{3}}}+{x}-{2}}}}}}$$ rocedwrp 2021-09-13 Answered

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