(1) Find the domain and range of each of the following ...
(1) Find the domain and range of each of the following functions please.
(a) [pic] (b) [pic]
(2) Evaluate each of the following limits please.
(a) [pic] (g) [pic]
(b) [pic][pic] (h) [pic]
(c) [pic] (i) [pic]
(d) [pic] (j) [pic]
(e) [pic] (k) [pic]
(f) [pic] (l) [pic]
(3) Find [pic] and simplify please.
(a) [pic] (i) [pic]
(b) [pic] (j) [pic]
(c) [pic] (k) [pic]
(d) [pic] (l) [pic]
(e) [pic] (m) [pic]
(f) [pic] (n) [pic]
(g) [pic] (o) [pic]
(h) [pic] (p)
(4) Find all relative max and min points if [pic]
(5) Find the volume of the largest right circular cylinder which may be inscribed in a sphere whose radius is 3 feet.
[pic]
(6)
(7) Find the value of [pic] at x = 1 for the function [pic] if [pic][pic][pic][pic][pic][pic]
(8) Write an equation of the line tangent to each of the following at the indicated point.
(a) [pic] at x = 1.
(b) [pic]
(c) [pic]
(9) Sketch a graph of [pic] showing all max/min points and all inflection points.
(10) Find all values of the constants a, b, and c if the graph of [pic] and [pic] are to be tangent to each other at the point (1 , 1).
(11) Solve each of the following differential equations please.
(a) [pic] , the graph of y passes through (2 , 3) with slope 0.
(b) [pic] , y passes through (1 , 4).
(12) Evaluate each of the following integrals please.
(a) [pic] (l) [pic]
(b) [pic] (m) [pic]
(c) [pic] (n) [pic]
(d) [pic] (o) [pic]
(e) [pic] (p) [pic]
(f) [pic] (q) [pic] [pic]
(g) [pic] (r) [pic]
(h) [pic] (s) [pic]
(i) [pic] (t) [pic]
(j) [pic] (u) [pic]
(k) [pic] (v) [pic]
Answers
(1) (a) (b)
(2) (a) [pic] (g) [pic]
(b) –32 [pic] (h) [pic]
(c) [pic] (i) [pic]
(d) [pic] (j) [pic]
(e) [pic] (k) [pic]
(f) [pic] (l) 2
Answers
(3) (a) [pic] (i) [pic]
(b) [pic] (j) [pic]
(c) [pic] (k) [pic]
(d) [pic] (l) [pic]
(e) [pic] (m) [pic]
(f) [pic]
(n) [pic]
(g) [pic] (o) [pic]
(h) [pic] (p) [pic]
(4) max. at [pic] , min. at (0 , 0)
(5) [pic]
Answers
(6) [pic]
(7) 180
(8) (a) [pic]
(b) y = 2
(c) [pic]
(9) Graph
(10) a = 2 , b = –2 , c = 2
(11) (a) [pic] (b) [pic]
Answers
(12) (a) [pic] + C (l) [pic] + C
(b) [pic] + C (m) [pic] + C
(c) [pic] + C (n) [pic] + C
(d) [pic] + C (o) [pic] + C
(e) [pic] + C (p) [pic] + C
(f) [pic] + C (q) [pic] + C
(g) [pic] + C (r) [pic] + C
(h) [pic] + C (s) [pic] + C
(i) [pic] + C (t) [pic] + C
(j) [pic] + C
(u) [pic] + C
(k) [pic] + C
(v) [pic] + C
-----------------------
[pic]
5
2
2
3
Water is pouring into the trough to the right at a constant rate of 2 cubic feet per minute. Each base is an inverted isosceles triangle with base 2 feet and height 3 feet as shown. How fast is the depth of the water changing at the instant when the trough is [pic] full by volume?
Domain: [pic]
Range: [pic]
Domain: [pic]
Range: y is real
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