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Four identical lightbulbs with the same resistance each are connected to an ideal battery as shown below. Bulb R2 is removed. How does the brightness of the remaining bulbs change? It might help to remember that the brightness of identical bulbs is an observable measure of the power dissipated by the bulbs.  

What is V1 − V2 in the circuit below? The arrows indicate the known values and directions for the current at their placements. The resistor R has unknown resistance.

What is \(\frac{\partial \cos(xyz)}{\partial x}\)?

Passage 2 Which of the following is implied based on the text?

Find the volume of the space beneath the graph of the function \(f(x,y)=\sqrt{1-x^2-y^2}\) over the unit disk.

Sketch the level curves and gradient vector field of the function \(f(x,y)=x^2+3y^2\)

A 19-year-old man complains of severe fatigue, sore throat, and swollen lymph nodes. Manual differential counts: WBC: 11.3                                      Band neutrophils: 8 RBC: 4.99                                       Segmented neutrophils: 12 Hgb: 16.1                                        Lymphocytes: 78 Hct: 49.0                                         Monocytes: 2 MCV: 98.2                                      Eosinophils: MCH: 32.3                                      Basophils: MCHC: 33.3                                   Metamyelocytes: RDW: 11.9                                     Myelocytes: PLT: 138.9                                      Promyelocytes: The pic below demonstrates many of the lymphocytes seen on the peripheral smear.      What additional test should be performed?    

What is \(\frac{\partial \cos(xyz)}{\partial x}\)?

Compute the gradient of the following function \(f(x,y,z)=xyz\).

Sketch the level curves and gradient vector field of the function \(f(x,y)=x^2+3y^2\)