Questions from Calculus

Q: The wave heights h in the open sea depend on the speed

The wave heights h in the open sea depend on the speed v of the wind and the length of time t that the wind has been blowing at that speed. Values of the function h = f (v, t) are recorded in feet in...

Q: Use the table in Example 3 to find a linear approximation to

Use the table in Example 3 to find a linear approximation to the heat index function when the temperature is near 948F and the relative humidity is near 80%. Then estimate the heat index when the temp...

Q: The wind-chill index W is the perceived temperature when the

The wind-chill index W is the perceived temperature when the actual temperature is T and the wind speed is v, so we can write W = f (T, v). The following table of values is an excerpt from Table 1 in...

Q: If z = x2 - xy + 3y2 and (x,

If z = x2 - xy + 3y2 and (x, y) changes from (3, -1) to (2.96, 20.95), compare the values of ∆z and dz.

Q: Use differentials to estimate the amount of metal in a closed cylindrical

Use differentials to estimate the amount of metal in a closed cylindrical can that is 10 cm high and 4 cm in diameter if the metal in the top and bottom is 0.1 cm thick and the metal in the sides is 0...

Q: Use differentials to estimate the amount of tin in a closed tin

Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and height 12 cm if the tin is 0.04 cm thick.

Q: The wind-chill index is modeled by the function

The wind-chill index is modeled by the function where T is the temperature (in 0C) and v is the wind speed (in km/h). The wind speed is measured as 26 km/h, with a possible error of 62 km/h, and the...

Q: In Exercise 14.1.39 and Example 14.3

In Exercise 14.1.39 and Example 14.3.3, the body mass index of a person was defined as B (m, h) = m/h2, where m is the mass in kilograms and h is the height in meters. Exercise 14.1.39: The body mas...

Q: (a). The function was graphed in Figure 4. Show

(a). The function was graphed in Figure 4. Show that fx (0, 0) and fy (0, 0) both exist but f is not differentiable at s0, 0d. [Hint: Use the result of Exercise 45.] Figure 4: Exercise 45: Prove...

Q: Find an equation of the tangent plane to the given surface at

Find an equation of the tangent plane to the given surface at the specified point. z = 2x2 + y2 - 5y, (1, 2, -4)