The italicized phrase before each sample problem indicates a similar problem in James Stewart. 2007. Essential Calculus: Early Transcendentals. Thomson Brooks/Cole: Belmont, CA.
Similar to 3.1.30:
3.1 Determine the limit: limx-->(pi/4)+ of [10^(3 sin 2x)] (Check to verify this is similar.)
Similar to 3.2.78:
3.2 Inverses and graphing
Suppose a curve is moved down 5 units. How would that move change its reflection about a line passing through the origin with a 45 degree positive slope? In answering this question, determine and use the inverse of g, g-1(x), where
g(x) = f(x) - 5 and f(x) is one-to-one.
Similar to 3.3.58:
3.3 Implicit differentiation
Assuming x^(x^2 + 3x) = y^(2x - 7), obtain y'.
Similar to 3.3.60ab:
3.4 Growth with an upper bound
In south Georgia when a certain Tupelo Gum tree's flower buds first open in the spring, bee hives in a 20 mile radius discover them according to this formula:
n(t) = 214 / [2 + 3 e^(-7t)],
where n(t) is the number of hives that have discovered the open flowers after t hours.
a. Compute limt-->+infinity n(t), and interpret the result in context.
b. Determine the rate at which hives are discovering the open flowers.
Similar to 3.4.10:
3.5 Half lives
0.0016 micrograms of the 259No isotope of nobelium decayed to 12.5 percent of that mass in 2 hours, 54 minutes.
a. Determine the half life of 259No.
b. If the 259No was created at 12 noon, at what time will only 5 percent of it remain?
Similar to 3.4.16:
3.6 Cooling/warming
Ice tea is 35 degrees F at noon when it is poured in a glass in a 70 degrees F room. When the tea is 50 degrees F, it is warming at rate of 0.5 degrees F / minute. At what time do these conditions exist?
Similar to 3.5.32:
3.7 Let csc-1 x denote the inverse cosecant of x, and suppose csc-1 (xy) = 5x - (x^3)y. Determine y'.
Similar to 3.5.40:
3.8 A sprinkler with a 45 second rotation is 20 feet from the nearest point P on a straight sidewalk. How fast is water from the sprinkler moving across the sidewalk when it is 5 feet from P?
Similar to 3.7.36:
3.9 Compute using the most efficient method. But if l'Hopital's rule could not be applied at all, explain why not.
limx-->pi+ [tan (x/4)] ^ [1/(x-pi)^2]
Similar to 3.7.48:
3.10 Solve for a and b.
limx-->0 [(1 - cos 2x) / x^4 + a + b/x^2] = 0
