Find the indicated partial sum of the series. $\sum_{i=1}^{\infty} \frac{7}{5^{i}}$ Fourth partial sum

What is partial derivative of f(x,y) with respect to x at (a,b)?

What is meant by partial pressure?

What is an nth partial sum?

Let T = g(x, y) be the temperature at the point (x, y) on the ellipse $x = 2 \sqrt { 2 } \cos t , \quad y = \sqrt { 2 } \sin t , \quad 0 \leq t \leq 2 \pi,$ and suppose that

$$\frac { \partial T } { \partial x } = y , \quad \frac { \partial T } { \partial y } = x.$$

Suppose that T = xy - 2. Find the maximum and minimum values of T on the ellipse.

Find $\frac{\partial}{\partial x} e^{\sqrt{1+5 y^{-23}}} \ln \left(1-17 y^{97} / z^{47}\right)$

Identify the type of curve for each equation, and then view it on a calculator.

$$4(y^2 + 6y + 1) = x(x - 4) - 24$$

Given the boundary-value problem

$$\begin{array}{ll}{\frac{\partial^{2} u}{\partial x^{2}}=\frac{\partial^{2} u}{\partial t^{2}},} & {0<x<1, \quad 0<t<1} \\ {u(0, t)=0,} & {u(1, t)=0, \quad 0 \leq t \leq 1}\end{array}$$

$u(x, 0)=x(1-x),\left.\quad \frac{\partial u}{\partial t}\right|_{t=0}=0, \quad 0 \leq x \leq 1$ use $h=k=\frac{1}{5}$ in equation (6) to compute the values of $u_{i, 1}$ by hand.

What is the opposite of a partial juror?

Compare partial monosomy with haploinsufficiency.

Determine whether the following statements are true and give an explanation or counterexample.

$\frac { \partial } { \partial x } \left( y ^ { 10 } \right) = 10 y ^ { 9 }$.

In view of Clapeyron's equation and figure, is there something special about ice $I$ versus the other forms of ice ?

Determine the partial derivative with respect to x and the partial derivative with respect to y at x=4 and y=1 for $f(x, y)=3x^2y^3+2x+3y^6+9$.

Solve the given problems.

If an observer and a source of sound are moving toward or away from each other, the observed frequency of sound is different from that emitted. This is known as the Doppler effect. The equation relating the frequency $f_0$ the observer hears and the frequency $f_s$ emitted by the source (a constant) is $f_0=f_s\left(\frac{v+v_0}{v-v_s}\right)$, where $v$ is the velocity of sound in air (a constant), $v_0$ is the velocity of the observer, and $v_s$ is the velocity of the source. Show that $f_s \frac{\partial f_0}{\partial v_s}=f_0 \frac{\partial f_0}{\partial v_0}$. Explain the meaning of $\partial f_0 / \partial v_s$.