Continuity

Practice Questions

AP Calculus BC › Continuity

Questions

Rational_graph

The graph above is a sketch of the function . For what intervals is continuous?

Rational_graph

The graph above is a sketch of the function . For what intervals is continuous?

Consider the piecewise function:

$y=\left{\begin{matrix} 1;: x<-5\0;:x>-5 \end{matrix}\right.$

What is $\lim_{x \to -5}$ ?

Consider the piecewise function:

$y=\left{\begin{matrix} 1;: x<-5\0;:x>-5 \end{matrix}\right.$

What is $\lim_{x \to -5}$ ?

Consider the function $f(x)=\frac{x^2-7x+12}{x-3}$ .

Which of the following statements are true about this function?

I. $f(x)\ is\ continuous\ at\ x = 3.$

II. $\lim_{x\to3}f(x)=-1$

III. $\lim_{x\to3}f(x)\ does\ not\ exist$

Consider the function $f(x)=\frac{x^2-7x+12}{x-3}$ .

Which of the following statements are true about this function?

I. $f(x)\ is\ continuous\ at\ x = 3.$

II. $\lim_{x\to3}f(x)=-1$

III. $\lim_{x\to3}f(x)\ does\ not\ exist$