1
warmup
Differential equations
Calculus
At t = 0 a current of 2 amperes flows in an RLC circuit with resistance R = 40 ohms,
inductance L = .2 henry s, and capacitance C = 10^{-5} farads. Find the current flowing in the circuit at
t > 0 if the initial charge on the capacitor is 1 coulomb. Assume that E(t) = 0 for t > 0.
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2
warmup
Multivariable calculus
Calculus
Sketch vector field \(\mathbf{G}(x, y, z) = \langle 2, \frac{z}{2}, 1 \rangle\).
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3
core
Parametric equations and vector functions
Calculus
\( \frac{x^2}{4} + \frac{y^2}{16} = 1 \)
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4
warmup
Parametric equations and vector functions
Calculus
$$x=e^{t}, \quad y=e^{2t}$$
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5
core
Parametric equations and vector functions
Calculus
\(x = 4 \cos(2\pi s), y = 3 \sin(2\pi s), s = -\frac{1}{4}\)
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6
core
Parametric equations and vector functions
Calculus
\( r = \frac{4}{1 + \cos \theta} \)
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