\(\displaystyle{d}=\sqrt{{{\left({x}–{2}\right)}^{{2}}+{y}^{{2}}}}=\sqrt{{{\left({x}-{2}\right)}^{{2}}+{\left(\sqrt{{x}}\right)}^{{2}}}}=\sqrt{{{x}^{{2}}–{4}{x}+{4}+{x}}}=\sqrt{{{x}^{{2}}–{3}{x}+{4}}}\)

asked 2021-11-13

Find the terminal point P(x, y) on the unit circle determined by the given value of t.

\(\displaystyle{t}={\frac{{{5}\pi}}{{{2}}}}\)

\(\displaystyle{t}={\frac{{{5}\pi}}{{{2}}}}\)

asked 2021-10-31

Find the point(s) on the surface at which the tangent plane is horizontal.

\(\displaystyle{z}={x}{y}+{\frac{{{1}}}{{{x}}}}+{\frac{{{1}}}{{{y}}}}\)

\(\displaystyle{z}={x}{y}+{\frac{{{1}}}{{{x}}}}+{\frac{{{1}}}{{{y}}}}\)

asked 2021-12-07

Find the point on the plane 2x-y+2z=20 nearest the origin.

asked 2021-11-11

Find the point on the line y = 3x + 4 that is closest to the origin.

asked 2021-10-18

Find the points on the cone \(\displaystyle{z}^{{2}}={x}^{{2}}+{y}^{{2}}\) that are closest to the point (4,2,0)

asked 2021-11-15

Find the point on the hyperbola xy = 8 that is closest to the point (3,0)

asked 2021-12-06

At what point does the curve have maximum curvature?

\(\displaystyle{y}={9}{\ln{{\left({x}\right)}}}\)

What happens to the curvature as \(\displaystyle{x}\to\infty\) ?

\(\displaystyle{y}={9}{\ln{{\left({x}\right)}}}\)

What happens to the curvature as \(\displaystyle{x}\to\infty\) ?