# A+ Work

1. The period T of a simple pendulum with small oscillations is calculated from the formula , where L is the length of the pendulum and g is the acceleration due to gravity. Suppose that the values of L and g have errors of at more 0.5% and 0.1%, respectively. Use a linear approximation to approximate the maximum percentage error in the calculated value of T.

2. Let (Polar coordinates).

a. Find . Be careful, . You will need to use the chain rule to find fx and fy. In class we derived the formulas and .

c. Find the equation (in rectangular coordinates) of the tangent plane to the surface at the point with rectangular coordinates (1, 1).

The equation of the tangent plane to the surface at the point with rectangular coordinates (1, 1) has the form:

3. Let (Spherical coordinates)

a. Find . Be careful, . You will need to use the chain rule to find fx , fy , and fz. You will also need to compute , , and . Use the equation . You will also need to compute , , and . Use the equation .

b. At the point with rectangular coordinates (1, 0, 1), find the direction of the maximum increase of f.

2. Let (Polar coordinates).

a. Find . Be careful, . You will need to use the chain rule to find fx and fy. In class we derived the formulas and .

c. Find the equation (in rectangular coordinates) of the tangent plane to the surface at the point with rectangular coordinates (1, 1).

The equation of the tangent plane to the surface at the point with rectangular coordinates (1, 1) has the form:

3. Let (Spherical coordinates)

a. Find . Be careful, . You will need to use the chain rule to find fx , fy , and fz. You will also need to compute , , and . Use the equation . You will also need to compute , , and . Use the equation .

b. At the point with rectangular coordinates (1, 0, 1), find the direction of the maximum increase of f.

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