(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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