2000002601
Level:
B
Consider the equation \(x^4+16=0\). Which of the given numbers is the solution of this equation?
\( 2(\cos{\frac{\pi}{4}}+ i \sin{\frac{\pi}{4}}) \)
\( 2i\)
\( -2i\)
\( 2(\cos{{\pi}}+ i \sin{{\pi}}) \)
B
2000002506
Level:
B
Simplify: \( \log_{10}(10!)-\log_{10}(9!) \)
\( 1\)
\( 10 \)
\( \log_{10}(9!) \)
\(0\)
2000002505
Level:
B
Simplify: \( \frac{(50-48)!}{(49-49)!} \)
\( 2 \)
\( 1 \)
\( 50! \)
\( \frac{50}{49} \)
2000002504
Level:
B
Simplify: \( \frac{50!}{49!+49!} \)
\( 25 \)
\( 100 \)
\( 49! \)
\( \frac{1}{49} \)
2000002503
Level:
B
Simplify: \( \frac{32!}{32 \cdot 31} \)
\( 30! \)
\( 31! \)
\( 29! \)
\( \frac{1}{31} \)
2000002502
Level:
B
Simplify: \( \frac{18!}{19!} \)
\( \frac{1}{19} \)
\( \frac{18}{19} \)
\( 18\)
\( 1 \)
2000002501
Level:
B
Simplify: \( \frac{8!}{6!} \)
\( 56\)
\( 336 \)
\( 8 \)
\(\frac{4}{3} \)
2000002405
Level:
B
Decide which of the functions is odd.
\( f(x) = \frac{5}{x} \)
\( f(x) = \frac{x^2}{x^2-4} \)
\( f(x) = \frac{x^2}{2-x} \)
\( f(x) =(x+1)^2 \)
2000002404
Level:
B
Decide which of the functions is even.
\( f(x) = -x^2 +3 \)
\( f(x) = \frac{x}{x^2} \)
\( f(x)=-2x^3 \)
\( f(x) = \frac{1}{x^2+3x} \)
2000002403
Level:
B
Find the domain of the function \( f(x)=\frac{1}{|x-3|}\).
\( \mathbb{R} \setminus \{3\} \)
\( \mathbb{R} \)
\( (3;\infty) \)
\( (-3;3) \)