Finding Functions Find differentiable functions and that satisfy the specified condition

Chapter 8, Problem 63

(choose chapter or problem)

Finding Functions Find differentiable functions f and g that satisfy the specified condition such that

\(\lim _{x \rightarrow 5} f(x)=0 \quad \text { and } \quad \lim _{x \rightarrow 5} g(x)=0 .\)

Explain how you obtained your answers. (Note: There are many correct answers.)

(a) \(\lim _{x \rightarrow 5} \frac{f(x)}{g(x)}=10\)

(b) \(\lim _{x \rightarrow 5} \frac{f(x)}{g(x)}=0\)

(c) \(\lim _{x \rightarrow 5} \frac{f(x)}{g(x)}=\infty\)

Text Transcription:

lim_x rightarrow 5  f(x)=0 and lim_rightarrow 5 g(x)=0

lim_x rightarrow 5  f(x)/g(x)=10

lim_x rightarrow 5  f(x)/g(x)=0

lim_x rightarrow 5  f(x)/g(x)=infinity