Questions from General Calculus

Q: Find dy/dx by implicit differentiation. cos(xy

Find dy/dx by implicit differentiation. cos(xy) = 1 + sin y

Q: Scientists can determine the age of ancient objects by the method of

Scientists can determine the age of ancient objects by the method of radiocarbon dating. The bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive isotope of carbon, 14...

Q: For any vectors u and v in V3, |u ×

For any vectors u and v in V3, |u × v | − |v × u |.

Q: Evaluate the upper and lower sums for f (x) =

Evaluate the upper and lower sums for f (x) = 1 + x2, -1 ≤ x ≤ 1, with n = 3 and 4. Illustrate with diagrams like Figure 14. Figure 14:

Q: With a programmable calculator (or a computer), it is possible

With a programmable calculator (or a computer), it is possible to evaluate the expressions for the sums of areas of approximating rectangles, even for large values of n, using looping. (On a TI use th...

Q: Find the point at which the line intersects the given plane.

Find the point at which the line intersects the given plane. 5x = y/2 = z + 2; 10x - 7y + 3z + 24 = 0

Q: With a programmable calculator (or a computer), it is possible

With a programmable calculator (or a computer), it is possible to evaluate the expressions for the sums of areas of approximating rectangles, even for large values of n, using looping. (On a TI use th...

Q: Some computer algebra systems have commands that will draw approximating rectangles and

Some computer algebra systems have commands that will draw approximating rectangles and evaluate the sums of their areas, at least if xi* is a left or right endpoint. (For instance, in Maple use leftb...

Q: (a) If f (x) = ln x,

(a) If f (x) = ln x, 1 ≤ x ≤ 4, use the commands discussed in Exercise 11 to find the left and right sums for n = 10, 30, and 50. (b) Illustrate by graphing the rectangles in part (a). (c) Show that t...

Q: The speed of a runner increased steadily during the first three seconds

The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower and upper estimates for the distance that she tr...