Test | Math Tests - Calculus Tests, Precalculus Tests, College Algebra Tests, Arithmetic Tests

$\mbox{None of the above}$

$L \ \mbox{is linear, since} \ L[cy]=cL[y].$

$L \ \mbox{is linear, since} \ L[y_1+y_2]=L[y_1]+L[y_2].$

$L \ \mbox{is nonlinear, since} \ L[cy]=cL[y] \ \mbox{and} \ L[y_1+y_2]=L[y_1]+L[y_2].$

$L \ \mbox{ is linear, since} \ L[cy]=cL[y] \ \mbox{and} \ L[y_1+y_2]=L[y_1]+L[y_2].$

	$\mbox{None of the above}$
	$e^{\beta x}\cos \alpha x, \ e^{\beta x}\sin \alpha x \ \mbox{are linearly dependent solutions on any interval.}$
	$e^{\alpha x}\cos \beta x, \ e^{\alpha x}\sin \beta x \ \mbox{are linearly dependent solutions on any interval.}$
	$e^{\beta x}\cos \alpha x, \ e^{\beta x}\sin \alpha x \ \mbox{are linearly independent solutions on any interval.}$
	$e^{\alpha x}\cos \beta x, \ e^{\alpha x}\sin \beta x \ \mbox{are linearly independent solutions on any interval.}$

	$\mbox{None of the above}$
	$W_1 \ \mbox{is not a vector space, because it is not closed under addition.}$
	$W_2 \ \mbox{is a vector space, because} \ {\bf 0} \ \mbox{is in} \ W_2$
	$W_2 \ \mbox{is a vector space, because it is closed under addition.}$
	$W_1 \ \mbox{is not a vector space, because} \ {\bf 0} \ \mbox{is not in} \ W_1$

Test!

	$\mbox{None of the above}$
	$y=c_1\sum_{n=0}^{\infty}\dfrac{1}{(2n)!}x^{2n}+c_2\sum_{n=0}^{\infty}\dfrac{(-1)^n}{(2n+1)!}x^{2n+1}$
	$y=c_1\sum_{n=0}^{\infty}\dfrac{(-1)^n}{(2n)!}x^{2n}+c_2\sum_{n=0}^{\infty}\dfrac{1}{(2n+1)!}x^{2n+1}$
	$y=c_1\sum_{n=0}^{\infty}\dfrac{(-1)^n}{(2n)!}x^{2n}+c_2\sum_{n=0}^{\infty}\dfrac{(-1)^n}{(2n+1)!}x^{2n+1}$
	$y=c_1\sum_{n=0}^{\infty}\dfrac{1}{(2n)!}x^{2n}+c_2\sum_{n=0}^{\infty}\dfrac{1}{(2n+1)!}x^{2n+1}$

	$\left [ \begin{array}{r} 0\\ 1\\ 0\\ 1 \end{array} \right ], \quad \left [ \begin{array}{r} 0\\ 0\\ 1\\ -1 \end{array} \right ], \quad \left [ \begin{array}{r} 0\\ 0\\ 0\\ 1 \end{array} \right ]$
	$\left [ \begin{array}{r} 1\\ 0\\ 0\\ 1 \end{array} \right ], \quad \left [ \begin{array}{r} 0\\ 1\\ 0\\ 1 \end{array} \right ], \quad \left [ \begin{array}{r} 0\\ 0\\ 1\\ -1 \end{array} \right ], \quad \left [ \begin{array}{r} 0\\ 0\\ 0\\ 1 \end{array} \right ]$
	$\left [ \begin{array}{r} 1\\ 0\\ 0\\ 1 \end{array} \right ], \quad \left [ \begin{array}{r} 0\\ 1\\ 0\\ 1 \end{array} \right ], \quad \left [ \begin{array}{r} 0\\ 0\\ 1\\ -1 \end{array} \right ]$
	$\mbox{None of the above}$
	$\left [ \begin{array}{r} 1\\ 0\\ 0\\ 1 \end{array} \right ], \quad \left [ \begin{array}{r} 0\\ 1\\ 0\\ 1 \end{array} \right ], \quad \left [ \begin{array}{r} 0\\ 0\\ 1\\ -1 \end{array} \right ], \quad \left [ \begin{array}{r} 1\\ 0\\ 0\\ 1 \end{array} \right ]$

	$\left \{ t\left [ \begin{array}{c} 1\\[3mm] \dfrac{2}{3+\sqrt{33}} \end{array} \right ]: t \ \mbox{is any real number} \right \}$
	$\left \{ t\left [ \begin{array}{c} \dfrac{4}{3+\sqrt{33}}\\[5mm] 1 \end{array} \right ]: t \ \mbox{is any real number} \right \}$
	$\mbox{None of the above}$
	$\left \{ t\left [ \begin{array}{c} \dfrac{2}{3+\sqrt{33}}\\[5mm] 1 \end{array} \right ]: t \ \mbox{is any real number} \right \}$
	$\left \{ t\left [ \begin{array}{c} 1\\[3mm] \dfrac{4}{3+\sqrt{33}} \end{array} \right ]: t \ \mbox{is any real number} \right \}$

	${\bf x}(t)=c_1e^{-3t}\left [\begin{array}{r}7\\[2mm]1\end{array}\right ] +c_2e^{5t}\left [\begin{array}{r}-1\\[2mm]2\end{array}\right ]$
	${\bf x}(t)=c_1e^{-3t}\left [\begin{array}{r}1\\[2mm]7\end{array}\right ] +c_2e^{5t}\left [\begin{array}{r}-1\\[2mm]1\end{array}\right ]$
	${\bf x}(t)=c_1e^{-3t}\left [\begin{array}{r}7\\[2mm]1\end{array}\right ] +c_2e^{5t}\left [\begin{array}{r}-1\\[2mm]1\end{array}\right ]$
	$\mbox{None of the above}$
	${\bf x}(t)=c_1e^{-3t}\left [\begin{array}{r}1\\[2mm]7\end{array}\right ] +c_2e^{5t}\left [\begin{array}{r}-1\\[2mm]2\end{array}\right ]$

	${\bf x}(t)=c_1\left [\begin{array}{r}-\cos 4t\\[2mm]\sin 4t\end{array}\right ] +c_2\left [\begin{array}{r}\sin 4t\\[2mm]-\cos 4t\end{array}\right ]$
	${\bf x}(t)=c_1\left [\begin{array}{r}-\cos 4t\\[2mm]\sin 4t\end{array}\right ] +c_2\left [\begin{array}{r}\sin 4t\\[2mm]\cos 4t\end{array}\right ]$
	$\mbox{None of the above}$
	${\bf x}(t)=c_1\left [\begin{array}{r}\cos 4t\\[2mm]\sin 4t\end{array}\right ] +c_2\left [\begin{array}{r}\sin 4t\\[2mm]\cos 4t\end{array}\right ]$
	${\bf x}(t)=c_1\left [\begin{array}{r}\cos 4t\\[2mm]\sin 4t\end{array}\right ] +c_2\left [\begin{array}{r}\sin 4t\\[2mm]-\cos 4t\end{array}\right ]$

	${\bf x}(t)=e^{2t}\left [\begin{array}{r}-2t(c_1+c_2)+c_1\\[2mm]2t(c_1+c_2)+c_1\end{array}\right ]$
	${\bf x}(t)=e^{2t}\left [\begin{array}{r}-2t(c_1+c_2)+c_1\\[2mm]2t(c_1+c_2)+c_2\end{array}\right ]$
	${\bf x}(t)=e^{2t}\left [\begin{array}{r}-2t(c_1-c_2)+c_2\\[2mm]2t(c_1+c_2)+c_2\end{array}\right ]$
	$\mbox{None of the above}$
	${\bf x}(t)=e^{2t}\left [\begin{array}{r}-2t(c_1-c_2)+c_1\\[2mm]2t(c_1+c_2)+c_2\end{array}\right ]$

	$X^{\prime}T^{\prime}=\alpha^2 X^{\prime\prime}T$
	$XT^{\prime}=\alpha^2 X^{\prime\prime}T$
	$X^{\prime}T=\alpha^2 X^{\prime\prime}T$
	$\mbox{None of the above}$
	$X^{\prime}T^{\prime}=\alpha^2 X^{\prime\prime}T^{\prime\prime}$

	$f(x)=\dfrac{1}{2}+\dfrac{4}{\pi^2}\sum_{n=1}^{\infty}\dfrac{\cos((2n-1)\pi x)}{(2n-1)^2}$
	$f(x)=\dfrac{1}{2}+\dfrac{4}{\pi^2}\sum_{n=1}^{\infty}\dfrac{\sin((2n-1)\pi x)}{(2n-1)^2}$
	$f(x)=\dfrac{1}{2}+\dfrac{4}{\pi^2}\sum_{n=1}^{\infty}\dfrac{\sin(2n\pi x)}{(2n)^2}$
	$f(x)=\dfrac{1}{2}+\dfrac{4}{\pi^2}\sum_{n=1}^{\infty}\dfrac{\cos(2n\pi x)}{(2n)^2}$
	$\mbox{None of the above}$