Questions from General Calculus

Q: Find the limit. limn→∞ ∑n i=1

Find the limit. limn→∞ ∑n i=1 3/n [ (1 + 3i/n)3 - 2 (1 + 3i/n)]

Q: Evaluate ∑ni-1 (2i + 2i).

Evaluate ∑ni-1 (2i + 2i).

Q: Write out the form of the partial fraction decomposition of the function

Write out the form of the partial fraction decomposition of the function (as in Example 7). Do not determine the numerical values of the coefficients.

Q: Evaluate ∑ni-1 [ ∑nj-1 (i

Evaluate ∑ni-1 [ ∑nj-1 (i + j).

Q: Use the definition of a hyperbola to derive Equation 2 for a

Use the definition of a hyperbola to derive Equation 2 for a hyperbola with foci (±c, 0).

Q: Suppose that P (x, y) is any point on

Suppose that P (x, y) is any point on the parabola with focus (0, p) and directrix y = -p. (See Figure 14 (below).) Use the definition of a parabola to show that x2 = 4py.

Q: (a). Find the foci and asymptotes of the hyperbola x2

(a). Find the foci and asymptotes of the hyperbola x2 – y2 = 1 and sketch its graph. (b). Sketch the graph of y2 – x2 = 1.

Q: Sketch the region bounded by the curves. x + 4y

Sketch the region bounded by the curves. x + 4y = 8 and x = 2y2 - 8

Q: Sketch the region bounded by the curves. y = 4

Sketch the region bounded by the curves. y = 4 – x2 and x – 2y = 2

Q: Let P (x1, y1) be a point on the

Let P (x1, y1) be a point on the ellipse x2/a2 + y2/b2 = 1 with foci F1 and F2 and let α and β be the angles between the lines PF1, PF2 and the ellipse as shown in the figure...