1103124502
Level:
C
Identify which of the graphs below represents the function \( f(x)=\left|\frac{1-2x}{x-4}\right|;\ x\in [-\frac52;\frac52] \).
C
1103124602
Level:
C
Let \( f(x)=\frac{x^2-x-6}{x^2-9} \). One of the following pictures shows a part of the graph of \( f \). Choose the picture.
1003118307
Level:
C
Identify which of the following functions has the maximum at \( x=-\frac12 \).
\( m(x)=-\left|\frac{4x+2}{x-2}\right| \)
\( g(x)=\left|-\frac{5x+10}{2x-1}\right| \)
\( f(x)=-\left|\frac{2x+1}{4x+2}\right| \)
\( h(x)=-\left|\frac{x+1}{2x-2}\right| \)
1003118306
Level:
C
Find the true statement about the function \( f(x)=\left|\frac{4x-4}{2x-1}\right| \).
The domain of the function \( f \) is the set \( \left(-\infty,\frac12\right)\cup\left(\frac12,\infty\right) \).
The range of the function \( f \) is the set \( [0,2)\cup(2,\infty) \).
The function \( f \) has the minimum at \( x=4 \).
The function \( f \) is an injective (one-to-one) function.
1003118305
Level:
C
Find the false statement about the function \( f(x)=\left|\frac1{2-3x}-3\right| \).
The domain of the function \( f \) is the set \( \left(-\infty,\frac32\right)\cup\left(\frac32,\infty\right) \).
The range of the function \( f \) is the interval \( \left[0,\infty\right) \).
The function \( f \) has the minimum at \( x=\frac59 \).
The function \( f \) is bounded below.
1003118304
Level:
C
Identify which of the following functions is bounded.
\( h(x)=\frac{3x-6}{2x-4} \)
\( f(x)=\frac{3x-6}{2x} \)
\( g(x)=3-\frac6{2x} \)
\( m(x)=\left|\frac{4x-3}{2x-6}\right| \)
1003047704
Level:
C
Find the limit. \[ \lim\limits_{n\to\infty}\frac{1^2+2^2+\dots+n^2}{n^2+7n-3} \]
Hint: \( 1^2+2^2+\cdots +n^2=\frac16 n(n+1)(2n+1) \).
\( \infty \)
\( 0 \)
\( \frac13 \)
\( -\frac13 \)
\( \frac16 \)
1003047703
Level:
C
Find the limit \( \lim\limits_{n\to\infty}\frac{\frac12+\frac14+\dots+\frac1{2^n}}{\frac13+\frac19+\dots+\frac1{3^n}} \).
\( 2 \)
\( \frac23 \)
\( \infty \)
\( 0 \)
\( \frac32 \)
1003047702
Level:
C
Find the limit:
\[ \lim\limits_{n\to\infty}\left(\frac13+\frac19+\dots+\frac1{3^n} \right) \].
\( \frac12 \)
\( \frac13 \)
\( \frac32 \)
\( \infty \)
\( \frac23 \)
1003047701
Level:
C
Find the limit \( \lim\limits_{n\to\infty}\frac{3+9+\dots+3^n}{4+16+\dots+4^n } \).
\( 0 \)
\( \frac32 \)
\( \infty \)
\( 1 \)
\( \frac34 \)