Unit 1 · Continuity · Defining a removable discontinuity
Let
\[f(x)=\begin{cases}\dfrac{x^2-4}{x-2},&x\ne 2,\\ k,&x=2.\end{cases}\]
For which value of \(k\) is \(f\) continuous at \(x=2\)?
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AP Calculus AB
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Unit 1 · Continuity · Defining a removable discontinuity
Let
\[f(x)=\begin{cases}\dfrac{x^2-9}{x-3},&x\ne 3,\\ k,&x=3.\end{cases}\]
For which value of \(k\) is \(f\) continuous at \(x=3\)?
Unit 1 · Continuity · Defining a removable discontinuity
Let
\[f(x)=\begin{cases}\dfrac{x^2-16}{x-4},&x\ne 4,\\ k,&x=4.\end{cases}\]
For which value of \(k\) is \(f\) continuous at \(x=4\)?
Unit 1 · Continuity · Defining a removable discontinuity
Let
\[f(x)=\begin{cases}\dfrac{x^2-25}{x-5},&x\ne 5,\\ k,&x=5.\end{cases}\]
For which value of \(k\) is \(f\) continuous at \(x=5\)?
Unit 1 · Continuity · Defining a removable discontinuity
Let
\[f(x)=\begin{cases}\dfrac{x^2-36}{x-6},&x\ne 6,\\ k,&x=6.\end{cases}\]
For which value of \(k\) is \(f\) continuous at \(x=6\)?
Unit 1 · Continuity · Intermediate Value Theorem
A function \(f\) is continuous on \([1,4]\), with \(f(1)=-2\) and \(f(4)=3\). Which conclusion is guaranteed?
Unit 1 · Continuity · Intermediate Value Theorem
A function \(f\) is continuous on \([2,5]\), with \(f(2)=-3\) and \(f(5)=4\). Which conclusion is guaranteed?
Unit 1 · Continuity · Intermediate Value Theorem
A function \(f\) is continuous on \([3,6]\), with \(f(3)=-4\) and \(f(6)=5\). Which conclusion is guaranteed?
Unit 1 · Continuity · Intermediate Value Theorem
A function \(f\) is continuous on \([4,7]\), with \(f(4)=-5\) and \(f(7)=6\). Which conclusion is guaranteed?
Unit 1 · Continuity · Intermediate Value Theorem
A function \(f\) is continuous on \([5,8]\), with \(f(5)=-6\) and \(f(8)=7\). Which conclusion is guaranteed?