3. [25 points] Consider the function given by the values in…

3. Consider the function given by the values in the table below.                                                           0 2 4 Find the Lagrange form and Newton form of the interpolating polynomial What is the degree of your interpolating polynomial? Expand out the Lagrange and Newton forms to verify whether they agree with each other. Explain why.

A 19-year-old gravid patient presents to the ultrasound depa…

A 19-year-old gravid patient presents to the ultrasound department with a history of light vaginal spotting and nausea. Sonographically, a single live intrauterine pregnancy is discovered. Within the right adnexa, a simple appearing cyst with a thick echogenic rim is noted. Interrogation with color Doppler reveals hyperemic flow within the borders of this mass. What is the most likely diagnosis?