Opiskelupolut
Opiskelupolut
Opiskelupolut
Juuri 13 Differentiaali- ja integraalilaskenta
Opiskelijapolut
Suositeltavia tehtäviä, saa ja voi laskea tietenkin muitakin tehtäviä.
1.1 Raja-arvo ja jatkuvuus (1 h)
|
TASO 1 (AS 5-6) |
101 102 103 104 105 106 107 |
|
TASO 2 (AS 7-8) |
101 102 103 104 105 106 107 108 109 110 111 112 113 115 |
|
TASO 3 (AS 9-10) |
101 102 103 104 105 106 107 108 109 110 111 112 113 115 116 117 118 120 |
1.2 Derivoituvuus ja jatkuvuus (2 h)
|
TASO 1 (AS 5-6) |
123 124 125 126 127 128 129 130 |
|
TASO 2 (AS 7-8) |
123 124 125 126 127 128 129 130 131 132 133 134 137 |
|
TASO 3 (AS 9-10) |
123 124 125 126 127 128 129 130 131 132 133 134 137 138 139 140 143 144 |
1.3 Raja-arvo äärettömyydessä (2 h)
|
TASO 1 (AS 5-6) |
150 151 152 153 154 155 156 157 |
|
TASO 2 (AS 7-8) |
150 151 152 153 154 154 155 156 157 158 159 160 161 162 163 164 166 167 |
|
TASO 3 (AS 9-10) |
150 151 152 153 154 154 155 156 157 158 159 160 161 162 163 164 166 167 171 173 174 |
2.1 Lukujonon raja-arvo (1 h)
|
TASO 1 (AS 5-6) |
201 202 203 204 205 |
|
TASO 2 (AS 7-8) |
201 202 203 204 205 206 207 208 209 210 211 212 213 |
|
TASO 3 (AS 9-10) |
201 202 203 204 205 206 207 208 209 210 211 212 213 215 217 |
2.2 Lukujonon monotonisuus (1 h)
|
TASO 1 (AS 5-6) |
232 233 234 235 236 237 238 |
|
TASO 2 (AS 7-8) |
232 233 234 235 236 237 238 239 240 241 242 244 245 248 250 251 252 |
|
TASO 3 (AS 9-10) |
232 233 234 235 236 237 238 239 240 241 242 243 246 247 249 251 252 253 254 255 257 258 259 |
2.3 Geometrisen lukujonon suppeneminen (1 h)
|
TASO 1 (AS 5-6) |
223 224 225 226 227 |
|
TASO 2 (AS 7-8) |
223 224 225 226 227 228 229 231 232 233 234 235 236 |
|
TASO 3 (AS 9-10) |
223 224 225 226 227 228 229 231 232 233 234 235 236 237 238 239 242 |
2.4 Sarja (2 h)
|
TASO 1 (AS 5-6) |
264 265 266 267 268 269 270 |
|
TASO 2 (AS 7-8) |
264 265 266 267 268 269 270 271 273 274 275 276 278 280 283 |
|
TASO 3 (AS 9-10) |
264 265 266 267 268 269 270 271 273 274 275 276 278 280 283 287 289 |
3.1 Epäoleellinen integraali (2 h)
|
TASO 1 (AS 5-6) |
301 302 303 304 305 306 |
|
TASO 2 (AS 7-8) |
301 302 303 304 305 306 307 308 310 311 313 |
|
TASO 3 (AS 9-10) |
301 302 303 304 305 306 307 308 310 311 312 313 316 317 318 320 321 322 324 327 |
3.2 Jatkuva jakauma (1 h)
|
TASO 1 (AS 5-6) |
330 331 332 333 334 335 |
|
TASO 2 (AS 7-8) |
330 331 332 333 334 335 336 337 338 340 341 342 |
|
TASO 3 (AS 9-10) |
330 331 332 333 334 335 336 337 338 340 341 342 343 345 348 |
4.1 Käänteisfunktio (1-2 h)
|
TASO 1 (AS 5-6) |
401 402 403 404 405 406 407 |
|
TASO 2 (AS 7-8) |
401 402 403 404 405 406 407 408 409 410 411 412 413 414 416 418 |
|
TASO 3 (AS 9-10) |
401 402 403 404 405 406 407 408 409 410 411 412 413 414 416 418 421 422 427 |
4.2 Kahden muuttujan funktio ja sen osittaisderivaatta (1-2 h)
|
TASO 1 (AS 5-6 ) |
428 429 430 431 432 433 434 |
|
TASO 2 (AS 7-8) |
428 429 430 431 432 433 434 435 436 437 439 440 441 443 447 448 450 |
|
TASO 3 (AS 9-10) |
428 429 430 431 432 433 434 435 436 437 439 440 441 443 447 448 450 453 454 456 |