Test 26
1.
\(a\in\mathbb R\)
\(f(x)=\begin{cases}\samefrac{2x+1}{x^2-4},&x<4\\\samefrac{3x-1}{5},&x\ge4\end{cases}\)
\(\lim_{x\to a}f(x)\ne f(a)\)
\(a=?\)
A) \(\{1,5\}\)B) \(\{-1,1\}\)C) \(\{2,3\}\)D) \(\{-2,2,4\}\)E) \(\{0,1\}\)
2.
\(a\in\mathbb R\)
\(f(x)=\begin{cases}\samefrac3{x-5},&x>5\\\samefrac{2x+1}{x^2-1},&x\le5\end{cases}\)
\(\lim_{x\to a}f(x)\ne f(a)\)
\(a=?\)
A) \(\{5\}\)B) \(\{-1,1\}\)C) \(\{-1,5\}\)D) \(\{1,5\}\)E) \(\{-1,1,5\}\)
3.
\(a\in\mathbb R\)
\(f(x)=\begin{cases}\samefrac{3x}{4},&x>-1\\\samefrac6{x^2+2},&x\le-1\end{cases}\)
\(\lim_{x\to a}f(x)\ne f(a)\)
\(a=?\)
A) \(\{-2\}\)B) \(\{-1\}\)C) \(\{0\}\)D) \(\{1\}\)E) \(\{4\}\)
4.
\(f(x)=\begin{cases}2x+4,&x\le0\\ax+b,&0<x<2\\x^2-1,&x\ge2\end{cases}\)
\(\lim_{x\to0}f(x)=f(0)\)
\(\lim_{x\to2}f(x)=f(2)\)
\(a+b=?\)
A) \(-\samefrac32\)B) \(-\samefrac12\)C) \(-1\)D) \(\samefrac72\)E) \(4\)
5.
\(f(x)=\begin{cases}x^3,&x\le2\\x^2+a,&x>2\end{cases}\)
\(\lim_{x\to2}f(x)=f(2)\)
\(a=?\)
A) \(1\)B) \(2\)C) \(3\)D) \(4\)E) \(5\)
6.
\(f(x)=\begin{cases}x^2+1,&x=-2\\x^3+a,&x\ne-2\end{cases}\)
\(\lim_{x\to-2}f(x)=f(-2)\)
\(a=?\)
A) \(5\)B) \(7\)C) \(9\)D) \(10\)E) \(13\)
7.
\(f(x)=\begin{cases}4x+3,&x<0\\a+4,&x=0\\x^3+3,&x>0\end{cases}\)
\(\lim_{x\to0}f(x)=f(0)\)
\(a=?\)
A) \(3\)B) \(2\)C) \(1\)D) \(0\)E) \(-1\)
8.
\(f(x)=\begin{cases}\samefrac{x^2+a}{x+2},&x\ne-2\\-4,&x=-2\end{cases}\)
\(\lim_{x\to-2}f(x)=f(-2)\)
\(a=?\)
A) \(-4\)B) \(-3\)C) \(-2\)D) \(2\)E) \(4\)