Question
Determine whether the statement is true or false..Finding Functions Find functions $f$ and $g$ such that $\lim _{x \rightarrow c} f(x)=\infty$ and $\lim _{x \rightarrow c} g(x)=\infty,$ but $\lim _{x \rightarrow c}[f(x)-g(x)] \neq 0$
Step 1
We can choose $f(x)=\frac{1}{x^{2}}$ and $g(x)=\frac{1}{x^{4}}$. Show more…
Show all steps
Your feedback will help us improve your experience
Carson Merrill and 84 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. Find functions $f$ and $g$ such that $\lim _{x \rightarrow c} f(x)=\infty$ and $\lim _{x \rightarrow c} g(x)=\infty$ but $\lim _{x \rightarrow c}[f(x)-g(x)] \neq 0$
Limits and Their Properties
Infinite Limits
Determine whether the statement is true or false. Explain your answer. $$ \begin{array}{l}{\text { If } \lim _{x \rightarrow a} f(x) \text { and } \lim _{x \rightarrow a} g(x) \text { exist, then so does }} \\ {\lim _{x \rightarrow a}[f(x)+g(x)]}\end{array} $$
LIMITS AND CONTINUITY
Computing Limits
Determine whether the statement is true or false. Explain your answer. $$ \begin{array}{l}{\text { If } \lim _{x \rightarrow a} f(x) \text { and } \lim _{x \rightarrow a} g(x) \text { both exist and are equal, }} \\ {\text { then } \lim _{x \rightarrow a}[f(x) / g(x)]=1}\end{array} $$
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD