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Pre-Algebra
Mean
Mode
Greatest Common Factor
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Order of Operations
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Mixed Fractions
Prime Factorization
Exponents
Radicals
Algebra
Combine Like Terms
Solve for a Variable
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Expand
Evaluate Fractions
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Evaluate
\frac{\pi x^{2}\sin(x)}{2}
Differentiate w.r.t. x
\frac{\pi x\left(x\cos(x)+2\sin(x)\right)}{2}
Graph
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Trigonometry
5 problems similar to:
2 \cdot \pi ( \frac { x } { 2 } ) ^ { 2 } \cdot \sin ( x )
Similar Problems from Web Search
Prove that x_{k}=2^{k} \cdot \sin \frac{\pi}{2^{k}} equals x_{1}'=2, x'_{2}=2 \sqrt{2}, x_{k+1}=x_{k} \sqrt{\frac{2x_{k}}{x_{k}+x_{k-1}}}
https://math.stackexchange.com/questions/528480/prove-that-x-k-2k-cdot-sin-frac-pi2k-equals-x-1-2-x-2
You can use that \cos (2x) = \cos^2 x - \sin^2 x, and hence 1 - \cos \frac{\pi}{2^k} = 1 - \cos^2 \frac{\pi}{2^{k+1}} + \sin^2 \frac{\pi}{2^{k+1}} = 2\sin^2 \frac{\pi}{2^{k+1}}. Then write \sqrt{\frac{2}{1+\cos \frac{\pi}{2^k}}} = \sqrt{\frac{2(1 - \cos \frac{\pi}{2^k})}{1 - \cos^2 \frac{\pi}{2^{k}}}} = \sqrt{\frac{4\sin^2 \frac{\pi}{2^{k+1}}}{\sin^2 \frac{\pi}{2^k}}} = \frac{2\sin \frac{\pi}{2^{k+1}}}{\sin \frac{\pi}{2^k}}, ...
Lipschitz-continuous f(x)=x^2\cdot \sin\left(\frac{1}{x}\right)
https://math.stackexchange.com/questions/618438/lipschitz-continuous-fx-x2-cdot-sin-left-frac1x-right
Notice that f'(x)=\begin{cases} 2x\sin\frac1x-\cos\frac1x &\text{ if } x\ne0\\ 0 &\text{ if } x=0 \end{cases}. Therefore |f'(x)|\le 2|x|\cdot\left|\sin\frac1x\right|+\left|\cos\frac1x\right|\le 3 \quad \forall x\ne 0. ...
Prove that x^\alpha \cdot\sin(1/x) is absolutely continuous on (0,1)
https://math.stackexchange.com/questions/294827/prove-that-x-alpha-cdot-sin1-x-is-absolutely-continuous-on-0-1
I assume that 1<\alpha<2. If not, as remarked by the questioner, f(x) is Lipschitz on (0,1) and the problem is simpler. You can use the following approach. Take a small \delta>0. You wish ...
Fourier transform of signal t \sin^2(t)/(\pi t)^2
https://math.stackexchange.com/questions/1598695/fourier-transform-of-signal-t-sin2t-pi-t2
HINTS: From the Convolution Theorem , we have \int_{-\infty}^\infty f(t)g(t)\,e^{i\omega t}\,dt=\frac{1}{2\pi}\int_{-\infty}^\infty F(\omega-\omega')G(\omega')\,d\omega' Setting f(t)=g(t)=\frac{\sin(t)}{\pi t} ...
Using the Fund. Theorem of Calc find h(x)=\int_{2}^\frac{1}{x}\sin^4tdt's derivative.
https://math.stackexchange.com/questions/3033249/using-the-fund-theorem-of-calc-find-hx-int-2-frac1x-sin4tdts-deri
Set \mathscr{F}'(x) : = \sin^4(x) , i.e., \mathscr{F} is the antiderivative of \sin^4(x) . Then by the fundamental theorem of calculus h(x) = \mathscr{F} \left( \frac{1}{x} \right) - \mathscr{F}\left( 2 \right). ...
Looking for a function f that is n-differentiable, but f^{(n)} is not continuous
https://math.stackexchange.com/q/58329
Let n be a positive integer and let f(x) = x^{2n} \cdot \sin\left(\frac{1}{x}\right) f(0) = 0 Then mathematical induction can be used to prove: (a) The nth derivative of f(x) exists for ...
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{ x } ^ { 2 } - 4 x - 5 = 0
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Linear equation
y = 3x + 4
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699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}
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