 Limits and continuity questions and answers

Recent questions in Limits and continuity Harold Kessler 2021-12-27 Answered

Let $$\displaystyle{f{{\left({x}\right)}}}={\frac{{{\left({x}+{8}\right)}^{{{2}}}}}{{{x}^{{{2}}}-{64}}}}$$. Find a) $$\displaystyle\lim_{{{x}\Rightarrow-{8}}}{f{{\left({x}\right)}}}$$, b) $$\displaystyle\lim_{{{x}\Rightarrow{0}}}{f{{\left({x}\right)}}}$$, and c) $$\displaystyle\lim_{{{x}\Rightarrow{8}}}{f{{\left({x}\right)}}}$$. skomminbv 2021-12-01 Answered

How do you find the limit as x approaches infinity of $$\displaystyle{y}={\arctan{{\left({e}^{{{x}}}\right)}}}$$? Redemitz4s 2021-11-24 Answered

Each limit represents the derivative of some function f at some number a. State such an f and a in each case. $$\displaystyle\lim_{{{t}\rightarrow{1}}}{\frac{{{t}^{{{4}}}-{t}-{2}}}{{{t}-{1}}}}$$ Elma Wilson 2021-11-21 Answered

Use continuity to evaluate the limit. $$\displaystyle\lim_{{{x}\to\pi}}{8}{\sin{{\left({x}+{\sin{{x}}}\right)}}}$$ Don't really understand this. My trig func, knowledge is low but an explanation to look back to always helps me move forward. rastafarral6 2021-11-21 Answered

Determine which of the following limits exist, and find the limits which do exists. a) $$\displaystyle\lim_{{{\left({x},{y}\right)}\to{\left({0},{0}\right)}}}{\frac{{{x}^{{3}}+{y}^{{3}}}}{{{x}^{{2}}+{y}^{{2}}}}}$$ b) $$\displaystyle\lim_{{{\left({x},{y}\right)}\to{\left({0},{0}\right)}}}{\frac{{{x}^{{2}}+{4}{x}{y}^{{2}}+{4}{y}^{{4}}}}{{{x}^{{2}}+{4}{y}^{{4}}}}}$$ puntgewelb5 2021-11-21 Answered

Evaluate the following limits. If you use l'Hospital's Rule, be sure to indicate when yyou are using it, and why it applies. a) $$\displaystyle\lim_{{{x}\to\infty}}{\left({3}\cdot{2}^{{{1}-{x}}}+{x}^{{2}}\cdot{2}^{{{1}-{x}}}\right)}$$ b) $$\displaystyle\lim_{{{x}\to{0}^{+}}}{\left({1}+{5}{x}\right)}^{{\frac{{2}}{{x}}}}$$ xcl3411 2021-11-20 Answered

Indeterminate forms $$\displaystyle{0}^{{0}}$$ and $$\displaystyle{1}^{\infty}$$. Evaluate the following limits. a) $$\displaystyle\lim_{{{x}\to{0}^{+}}}{x}^{{x}}$$ b) $$\displaystyle\lim_{{{x}\to\infty}}{\left({1}+{\frac{{{1}}}{{{x}}}}\right)}^{{x}}$$ jippie771h 2021-11-19 Answered

Evaluate the following limits. If needed, enter 'infinity' for $$\displaystyle\infty$$ and '-infinity' for $$\displaystyle-\infty$$ a) $$\displaystyle\lim_{{{x}\to{\frac{{{9}}}{{{2}}}}^{+}}}{\left({\frac{{{29}{x}}}{{{9}-{2}{x}}}}\right)}$$ b) $$\displaystyle\lim_{{{x}\to{\frac{{{9}}}{{{2}}}}^{{-}}}}{\left({\frac{{{29}{x}}}{{{9}-{2}{x}}}}\right)}$$ khi1la2f1qv 2021-11-18 Answered

Use continuity and the intermediate value theorem to solve problems. If $$\displaystyle{f{{\left({x}\right)}}}={x}^{{3}}-{6}{x}+{8}$$, show that there are values c for which f(c) equals a)$$\displaystyle\pi$$, b) $$\displaystyle-\sqrt{{{3}}}$$, and c) 6,000,000. varaderiyw 2021-11-18 Answered

Use the definition of continuity and the properties of limits to show that the function is continuous on the given interval. $$\displaystyle{f{{\left({x}\right)}}}={\frac{{{2}{x}+{3}}}{{{x}-{2}}}},\ {\left({2},\infty\right)}$$ korporasidn 2021-11-17 Answered

Evaluate the limit, if it exists. $$\displaystyle\lim_{{{x}\to{9}}}{\frac{{{3}-\sqrt{{{x}}}}}{{{9}{x}-{x}^{{2}}}}}$$ Tomasettiq3 2021-11-16 Answered

Evaluate the following limits. a) $$\displaystyle\lim_{{{x}\to{\frac{{{3}}}{{{8}}}}^{+}}}{\frac{{{20}{x}}}{{{3}-{8}{x}}}}$$ b) $$\displaystyle\lim_{{{x}\to{\frac{{{3}}}{{{8}}}}^{{-}}}}{\frac{{{20}{x}}}{{{3}-{8}{x}}}}$$ alka8q7 2021-11-16 Answered

So, I need to determine the end behavior of P for this equation: $$\displaystyle{P}{\left({x}\right)}=-{x}^{{5}}+{3}{x}^{{2}}+{x}$$ If possible, how is this done? zachutnat4o 2021-11-15 Answered

Let f(x,y)=\begin{cases}\frac{xy}{2x^2+3y^2},(x,y)\ne(0,0)\\0,(x,y)=(0,0)\end{cases} Discuss continuity of f(x,y) and existence of first order partial derivateves. Tammy Fisher 2021-11-14 Answered

Find the limit (if it exists). $$\displaystyle\lim_{{{x}\to{7}^{+}}}{\ln{{\left({x}-{7}\right)}}}$$ urca3m403 2021-11-14 Answered

If $$\displaystyle{4}\leq{x}{g{{\left({x}\right)}}}\leq{2}{x}^{{4}}-{2}{x}^{{2}}+{4}$$ for all x, evaluate $$\displaystyle\lim_{{{x}\to{1}}}{g{{\left({x}\right)}}}$$ jeliceg2 2021-11-13 Answered

Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why. lim x tends to 0 $$\displaystyle{e}^{{x}}-{1}-{\frac{{{x}}}{{{x}^{{2}}}}}$$ Minerva Kline 2021-11-12 Answered

Determine the one-sided limits numerically or graphically. If infinite, state whether the one-sided limits are oo or -oo, and describe the corresponding vertical asymptote. $$\displaystyle\lim_{{{x}\to{0}^{\pm}}}{\frac{{{x}-{\sin}{\left|{x}\right|}}}{{{x}^{{3}}}}}$$ sputavanomr 2021-11-11 Answered

Discuss the continuity and differentiability of the function g(t) at t=1, where g(t)=\begin{cases}t^3,&t\leq1\\t,&t>1\end{cases} alesterp 2021-11-10 Answered

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