Questions from General Calculus

Q: Find the cosine of the angle between the planes x + y

Find the cosine of the angle between the planes x + y + z = 0 and x + 2y + 3z = 1.

Q: In someone infected with measles, the virus level N (measured

In someone infected with measles, the virus level N (measured in number of infected cells per mL of blood plasma) reaches a peak density at about t = 12 days (when a rash appears) and then decreases f...

Q: The table shows the number of people per day who died from

The table shows the number of people per day who died from SARS in Singapore at two-week intervals beginning on March 1, 2003. (a) By using an argument similar to that in Example 4, estimate the num...

Q: Dinosaur fossils are often dated by using an element other than carbon

Dinosaur fossils are often dated by using an element other than carbon, such as potassium-40, that has a longer half-life (in this case, approximately 1.25 billion years). Suppose the minimum detectab...

Q: Determine whether the planes are parallel, perpendicular, or neither.

Determine whether the planes are parallel, perpendicular, or neither. If neither, find the angle between them. (Round to one decimal place.) 9x - 3y + 6z = 2, 2y = 6x + 4z

Q: (a) Express the area under the curve y = x5

(a) Express the area under the curve y = x5 from 0 to 2 as a limit. (b) Use a computer algebra system to find the sum in your expression from part (a). (c) Evaluate the limit in part (a).

Q: Find the exact area of the region under the graph of y

Find the exact area of the region under the graph of y = e-x from 0 to 2 by using a computer algebra system to evaluate the sum and then the limit in Example 3(a). Compare your answer with the estimat...

Q: Find the exact area under the cosine curve y = cos x

Find the exact area under the cosine curve y = cos x from x = 0 to x = b, where 0 ≤ b ≤ π/2. (Use a computer algebra system both to evaluate the sum and compute the limit.) In particular, what is the...

Q: (a) By reading values from the given graph of f

(a) By reading values from the given graph of f, use five rectangles to find a lower estimate and an upper estimate for the area under the given graph of f from x = 0 to x = 10. In each case sketch th...

Q: (a) Use six rectangles to find estimates of each type

(a) Use six rectangles to find estimates of each type for the area under the given graph of f from x = 0 to x = 12. (i) L6 (sample points are left endpoints) (ii) R6 (sample points are right endpoints...