Math 211 Business Calculus Applications of Derivatives

More documents

Recommendations

Info

$Math 229 Summation Worksheet$

$Math 211 Business Calculus - Department of Mathematical Sciences ...$

$Math 230 Practice Exam 1 Solutions$

$Math 210 Lecture Notes - Department of Mathematical Sciences ...$

– p. 6/34 Horizontal Asymptotes To find horizontal asymptotes compute the limit asx → ∞ (or−∞) Example: Consider the function f(x) = 5x3 +4x−8 x 3 −2x 2 −3x Find the horizontal asymptotes <strong>of</strong> f(x) Solution: Compute the limit 5x 3 +4x−8 lim f(x) = lim x→∞ x→∞x 3 −2x 2 −3x
Horizontal Asymptotes To find horizontal asymptotes compute the limit asx → ∞ (or−∞) Example: Consider the function f(x) = 5x3 +4x−8 x 3 −2x 2 −3x Find the horizontal asymptotes <strong>of</strong> f(x) Solution: Compute the limit 5x 3 +4x−8 1/x 3 lim f(x) = lim x→∞ x→∞x 3 −2x 2 −3x 1/x 3 – p. 6/34
Page 1 and 2: - p. 1/34 Math 211 Business Calculu
Page 3 and 4: - p. 2/34 Asymptotes A nonvertical
Page 11 and 12: - p. 3/34 Example Lety = f(x) = x+
Page 13 and 14: Example Lety = f(x) = x+ 1 x f ′
Page 23 and 24: - p. 4/34 Graph of x+1/x ♣ (1,2)
Page 25 and 26: Graph of x+1/x 1 lim x→0 + x =
Page 27 and 28: - p. 4/34 Graph of x+1/x 1 lim x→
Page 29 and 30: - p. 4/34 Graph of x+1/x 1 lim x→
Page 31 and 32: - p. 5/34 Vertical Asymptotes To fi
Page 41 and 42: - p. 6/34 Horizontal Asymptotes To
Page 47: Horizontal Asymptotes To find horiz
Page 55 and 56: - p. 7/34 Computing Limits When fin
Page 61 and 62: - p. 8/34 Example 1. Compute the li
Page 63 and 64: Example 1. Compute the limit x 2 +8
Page 65 and 66: - p. 8/34 Example 1. Compute the li
Page 67 and 68: - p. 9/34 Second example This limit
Page 69 and 70: Second example This limit may end u
Page 71 and 72: - p. 9/34 Second example This limit
Page 73 and 74: - p. 10/34 Graphs with asymptotes S
Page 75 and 76: Graphs with asymptotes Sketch the g
Page 77 and 78: Graphs with asymptotes Sketch the g
Page 79 and 80: - p. 11/34 Graphs continued Since t
Page 81 and 82: Graphs continued Since the first de
Page 83 and 84: Graphs continued Since the first de
Page 85 and 86: - p. 11/34 Graphs continued Since t
Page 87 and 88: - p. 12/34 Find the Asymptotes For
Page 89 and 90: Find the Asymptotes For y = f(x) =
Page 91 and 92: Find the Asymptotes For y = f(x) =
Page 99 and 100:
- p. 12/34 Find the Asymptotes For
Page 101 and 102:
Graph of (x−2)/(x+1) - p. 13/34
Page 103 and 104:
- p. 13/34 Graph of (x−2)/(x+1) x
Page 105 and 106:
- p. 13/34 Graph of (x−2)/(x+1) x
Page 107 and 108:
- p. 13/34 Graph of (x−2)/(x+1) x
Page 109 and 110:
- p. 14/34 Business Applications Th
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
- p. 16/34 Maximize Revenue If the
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
- p. 17/34 Max versus Min R = −0.
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
- p. 18/34 Maximize Revenue The rev
Page 141 and 142:
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
- p. 19/34 Max versus Min R = x 3
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
- p. 20/34 Maximize Profit As a gen
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
- p. 21/34 Maximize Profit Example
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
Page 189 and 190:
Page 191 and 192:
What level of sales maximizes profi
Page 193 and 194:
- p. 22/34 Ticket Sales Problem •
Page 195 and 196:
Page 197 and 198:
Page 199 and 200:
- p. 23/34 Ticket Sales Setup Letx=
Page 201 and 202:
Page 203 and 204:
Page 205 and 206:
- p. 24/34 Ticket Sales Solution R(
Page 207 and 208:
Page 209 and 210:
Page 211 and 212:
Page 213 and 214:
Page 215 and 216:
- p. 25/34 Dog Kennel Problem The o
Page 217 and 218:
Page 219 and 220:
Page 221 and 222:
- p. 26/34 Dog Kennel Setup Letx=le
Page 223 and 224:
Page 225 and 226:
Page 227 and 228:
- p. 27/34 Dog Kennel Solution Solv
Page 229 and 230:
Page 231 and 232:
Page 233 and 234:
Page 235 and 236:
Page 237 and 238:
Page 239 and 240:
- p. 28/34 Another Fencing Problem
Page 241 and 242:
Page 243 and 244:
Page 245 and 246:
Another Fencing Problem The owner o
Page 247 and 248:
- p. 29/34 Fencing Problem Setup Le
Page 249 and 250:
Page 251 and 252:
Page 253 and 254:
Page 255 and 256:
- p. 30/34 Fence Solution Solve xy
Page 257 and 258:
Page 259 and 260:
Fence Solution Solve xy = 810 fory:
Page 261 and 262:
Page 263 and 264:
Page 265 and 266:
Page 267 and 268:
Page 269 and 270:
- p. 31/34 Limit Def Revisited Reca
Page 271 and 272:
Page 273 and 274:
Page 275 and 276:
- p. 32/34 Marginal Revenue, Profit
Page 277 and 278:
Page 279 and 280:
Page 281 and 282:
Page 283 and 284:
- p. 33/34 Marginal Example Flying
Page 285 and 286:
Page 287 and 288:
Page 289 and 290:
Page 291 and 292:
Page 293 and 294:
Page 295 and 296:
- p. 34/34 Marginal Example Continu
Page 297 and 298:
Page 299 and 300:
Page 301 and 302:
Page 303 and 304:
Page 305 and 306:
Page 307:
show all

Math 211 Business Calculus Applications of Derivatives

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?