Questions from General Calculus

Q: If f (s, t) = sin s cos 2t

If f (s, t) = sin s cos 2t, find ∂f/∂s and ∂f/∂t.

Q: If z = sin wt, find ∂z/∂w and

If z = sin wt, find ∂z/∂w and ∂z/∂t.

Q: If f (s, t) = t sin st,

If f (s, t) = t sin st, find ∂f/∂s and ∂f/∂t.

Q: The identity sin (s + t) = sin s cos

The identity sin (s + t) = sin s cos t + cos s sin t was given in Section 8.2. Compute the partial derivative of each side with respect to t, and obtain an identity involving cos (s + t).

Q: Let f (p, q) = 1 - p(

Let f (p, q) = 1 - p(1 + q). Find ∂f/∂q and ∂f/∂p.

Q: Find the equation of the line tangent to the graph of y

Find the equation of the line tangent to the graph of y = tan t at t = π/4.

Q: Sketch the graph of y = t + sin t for 0

Sketch the graph of y = t + sin t for 0 ≤ t ≤ 2π.

Q: Find the area under the curve y = 2 + sin 3t

Find the area under the curve y = 2 + sin 3t from t = 0 to t = π/2.

Q: Find the area of the region between the curve y = sin

Find the area of the region between the curve y = sin t and the t-axis from t = 0 to t = 2π.

Q: Find the area of the region between the curve y = cos

Find the area of the region between the curve y = cos t and the t-axis from t = 0 to t = 3π/2.