미적분
0001
50002
20003
풀이 2쪽0004
풀이 2쪽0005
음의 무한대로 발산0006
수렴, 00007
수렴, 00008
발산(진동)0009
20010
40011
-30012
-30013
160014
60015
-50016
alpha+30017
2alpha-beta0018
alpha^2beta0019
2alpha/5beta0020
10021
00022
30023
3 1/0024
수렴, 1/30025
수렴, -20026
수렴, 00027
수렴, 00028
발산0029
발산0030
발산0031
발산0032
수렴, 1/20033
수렴, -30034
발산0035
수렴, 10036
㈎ 3 ㈏ 30037
40038
㈎ 0 ㈏ 00039
00040
수렴0041
발산0042
발산0043
수렴0044
발산0045
수렴0046
00047
10048
수렴, 20049
수렴, 1/30050
수렴, -10051
발산0052
-1/2<r_<1/20053
-3_<r<30054
-4<r_<40055
④0056
ㄱ, ㄹ0057
ㄱ: 0, ㄷ: 50058
-1/30059
①0060
230061
10062
30063
①0064
⑤0065
⑤0066
③0067
30068
①0069
②0070
30071
10072
③0073
20074
80075
-50076
②0077
③0078
1220079
1220080
120081
④0082
③0083
20084
②0085
④0086
-40087
60088
④0089
⑤0090
00091
⑤0092
①0093
ㄱ, ㄷ0094
②0095
ㄴ, ㄷ0096
③0097
③0098
60099
20100
5/20101 ③~
0102
③0103
④0104
80105
③0106
②0107
⑤0108
①0109
③0110
90111
-20112
~f(x)=i
x^2-20x
(0<x<1) (x=1) (x>1)
0113
④0114
⑴ a_n=216ns^2+16xn+5x ⑵ 1/40115
20116
①0117
2/30118
④0119
③0120
-3/20121
①0122
30123
r=1일 때 -1/4, r>1일 때 1/r0124
⑤0125
20126
120127
②0128
1/60129
②0130
4/50131
20132
②0133
330134
⑤0135
1/40136
-20137
⑤0138
20139
④0140
1/20141
50142
⑴ S_n= n(n+1)2 ⑵ 발산 ⑶ 발산0143
⑴ S_n=1-(1/2)^^n ⑵ 수렴 ⑶ 수렴, 10144
발산0145
발산0146
발산0147
수렴, 5/30148
⑴ S_n= nn/+1 ⑵ 1 ⑶ 10149
㈎ n/n+1 ㈏ 10150
풀이 16쪽0151
풀이 16쪽0152
풀이 16쪽0153
풀이 17쪽0154
20155
40156
10157
140158
수렴, 1/20159
수렴, 10/110160
발산0161
수렴, 3+13 20162
발산0163
수렴, 14/50164
발산0165
수렴, 2+12 20166
5/60167
-2/70168
5/20169
40170
-1/2<x<1/20171
-3<x<30172
0<x<20173
⑴ a_1=1/4, a_2=1/16, a_3=164 ⑵ 1/ /4 ⑶ 1/30174
㈎ 12/030 ㈏ 11/00 ㈐ 21/030 ㈑ 11/00 ㈒ 23/990175
152/9990176
13/900177
③0178
10179
20180
6 1/0181
1/40182
②0183
3/40184
1/120185
④0186
20187
1/20188
③0189
수렴, 00190
④0191
⑤0192
10193
③0194
-1/40195
④0196
②0197
⑤0198
30199
②0200
③0201 11/15
0202
2 /10203
7/150204
②0205
pai/60206
-8/810207
⑤0208
④0209
pai/4<theta<3/4pai0210
40211
4<x<50212
③0213
④0214
②0215
①0216
①0217
10218
③0219
(2/5, 4/5)0220
2/30221
30222
16(12 +1)0223
2(2+13 )0224
④0225
③0226
4/3pai0227
130228
4/3(pai-2)0229
50`cm0230
④0231
135/20232
①0233
③0234
27000235
1/80236
1/20237
⑤0238
①0239
215 50240
1/3<x_<3/50241
①0242
3/20243
-10244
ㄱ, ㄴ0245
13/80246
④0247
30248
①0249
①0250
20/70251
6`kg0252
1/20253
①0254
④0255
②0256
1/50257
inf0258
00259
00260
inf0261
10262
5/20263
10264
-inf0265
-inf0266
inf0267
inf0268
-inf0269
00270
-10271
-inf0272
20273
e0274
e0275
1/e0276
e^30277
20278
1/20279
-10280
ln~60281
20282
30283
ln~510284
ln~20285
y'=5e^x0286
y'=ex+20287
y'=ex-10288
y'=x(x+2)e^x0289
y'=ln~6.c16^x0290
y'=2~ln~4.c14^x0291
y'=-3~ln~2.c1(1/2)^^x0292
y'=3^x{(3x+1)ln~3+3}0293
y'=3/5x0294
y'=1/x0295
y'=2/x0296
y'=ln~x+10297
y'= 1x~ln~100298
y'= 1x~ln~20299
y'=log_5~x+ 1 ln~50300
y'=e^x(log_3x+ 1x~ln~3 )0301 -1
0302
④0303
30304
⑤0305
-10306
②0307
00308
②0309
②0310
10000311
⑤0312
e^6+ 1e^20313
②0314
1/e0315
1e^5
0316
③0317
1e^2
0318
③0319
50320
20321
②0322
②0323
2/50324
3~ln~210325
- 3 ln~30326
①0327
ln~1010328
①0329
2/50330
②0331
e0332
120333
③0334
10335
⑤0336
1/2~ln~50337
a=2/3, b=00338
a=0, b=2~ln~30339
80340
⑤0341
-80342
ln~210343
④0344
1/20345
④0346
ln~410347
20348
60349
③0350
4~ln~20351
①0352
60353
3e0354
1/20355
②0356
④0357
②0358
50359
a=e^3, b=10360
10361
①0362
100363
e^70364
③0365
-20366
②0367
40368
②0369
80370
90371
⑤0372
180373
⑤0374
①0375
20376
②0377
⑤0378
④0379
③0380
20381
5~ln~20382
⑴ -13/5 ⑵ 13/12 ⑶ -12/50383
csc~theta=12 , sec~theta=-12 , cot~theta=-10384
csc~theta=-2, sec~theta=- 213 3 , cot~theta=130385
csc~theta=2, sec~theta=- 213 3 , cot~theta=-130386
csc~theta=- 213 3 , sec~theta=2, cot~theta=-1330387
- 215 50388
110q30389
10390
16 -1240391
12 -1640392
2+130393
1220394
1/20395
130396
sin~2alpha=24/25, cos~2alpha=7/25, tan~2alpha=24/70397
12~~sin(theta+pai/4)0398
2~sin(theta+pai/6)0399
2~sin(theta+5/3pai)0400
132 0401 1/20402
1220403
20404
20405
-10406
1/20407
30408
50409
2/30410
y'=cos~x0411
y'=1-3~sin~x0412
y'=-cos~x+2~sin~x0413
y'=1/2~cos~x-1/x0414
y'=2~sin~x~cos~x0415
y'=cos~x-x~sin~x0416
y'=e^x(sin~x+cos~x)0417
y'=cos^2~x-sin^2~x0418
⑤0419
90420
- 513 30421
③0422
2~cot~theta+20423
⑤0424
④0425
④0426
169360427
-9/40428
②0429
1320430
④0431
④0432
2 110q-290433
②0434
①0435
10436
②0437
pai/60438
-10439
pai/40440
-180441
③0442
③0443
- 412 +79
0444
-40445
3/50446
①0447
65/120448
70449
③0450
2170451
30452
100453
60454
③0455
00456
1/20457
③0458
1pai/800459
⑤0460
10461
1/20462
②0463
10464
9/20465
-20466
②0467
②0468
-1/20469
-pai/40470
2/30471
③0472
②0473
1/20474
⑤0475
④0476
00477
10478
2/30479
②0480
60481
②0482
10483
-20484
④0485
3/2pai0486
④0487
120488
-20489
10490
⑤0491
①0492
④0493
-10494
④0495
②0496
pai/40497
-120/1190498
4/pai0499
00500
③0501 ①
0502
-30503
15 -120504
④0505
②0506
②0507
1/30508
③0509
80510
40511
⑤0512
119130513
20514
①0515
300516
③0517
y'=- 3(3x+2)^2
0518
y'=- 3x^2+1(x^3+x)^20519
y'=- e^x(e^x+1)^2
0520
y'=- 1x(ln~x)^2
0521
y'= 11(4x+3)^2
0522
y'= -x^2+1(x^2+1)^20523
y'= 2^x(x~ln~2+3~ln~2-1)(x+3)^20524
y'= 1-ln~xx^2~ln~30525
y'=- 1x^20526
y'=- 3x^40527
y'=2x- 2x^30528
y'=- 3x^4 +4x^5
0529
y'=2~cos~x+sec^2~x0530
y'=sec~x~tan~x-csc~x~cot~x219 라이트센미적분빠른정답찾기_ok.indd 1 18. 8. 29. 오후 4:45
0990
30991
①0992
-20993
3(x-4)1x+2z +C 2/0994
⑤0995
-10996
⑤0997
~f(x)= 23~ln~3 (3^x+8)23^x+8x0998
30999
21000
②1001 ②
1002
③1003
4/31004
21005
①1006
③1007
~f(x)=e5x+21008
③1009
x^2+x+6~ln|x-1|+C1010
-x+4~ln|x+1|+C1011
①1012
①1013
-121014
③1015
②1016
2e1017
1/2e^x(cos~x+sin~x)+C1018
(2-x^2)cos~x+2x~sin~x+C1019
②1020
3e-71021
151022
31023
②1024
②1025
④1026
⑤1027
③1028
①1029
51030
11031
④1032
ln~3(e+1)1033
②1034
③1035
ln~2+3/41036
6pai- 713 5/ 21037
~f(x)=ln|sin~x+cos~x|+21038
④1039
①1040
181041
ln~71042
e^3-1/e1043
16ln~21044
1/21045
13 -11046
631047
6ln~3 - 2ln~2
1048
2(e^4- 1e^2)1049
2pai^21050
01051
-21052
251053
7/21054
213 -2/31055
12481056
1/2(e^5-e^3)1057
ln~21058
1/41059
ln~2/31060
㈎ cos~theta ㈏ 0 ㈐ pai/2 ㈑ 1/2~sin~2theta+theta ㈒ pai/41061
pai/41062
21063
e^2+11064
11065
21066
x~sin~x1067
2x+5x^2+2x-3
1068
lnx+1/x1069
e^x(1- 1e^2)1070
~f(x)=-2~sin~~x1071
~f(x)=e^x-3^x~ln~31072
~f(x)=1/x- 1x^21073
-11074
e1075
e1076
pai^241077
②1078
21079
④1080
3/51081
②1082
4-1/e1083
81084
②1085
51086
⑤1087
1-1/e1088
2-pai/21089
e+e-2 /11090
③1091
③1092
②1093
01094
31095
④1096
①1097
4(e-1/e)1098
④1099
④1100
51101 26/3
1102
④1103
21104
⑤1105
5 /11106
21107
③1108
13 2 +pai/31109
⑤1110
⑤1111
41112
1/21113
61114
01115
③1116
~f(x)=1/x- 1e/-21117
e^2+e1118
②1119
②1120
121121
①1122
691123
④1124
e^31125
-1/41126
⑤1127
36/51128
3/2-4~ln~21129
4/3pai1130
②1131
③1132
pai1133
2 /31134
③1135
②1136
4~ln~2-21137
④1138
2/pai1139
②1140
②1141
213 31142
⑤1143
13 +pai/61144
21145
④1146
91147
51148
pai/21149
⑤1150
④1151
1+ 1e^21152
④1153
①1154
③1155
e^2+31156
⑤1157
㈎ 1/n ㈏ k/n ㈐ 11158
41159
㈎ pai/n ㈏ kpain ㈐ pai1160
ln~3/21161
㈎ _< ㈏ _> ㈐ -e^x+1 ㈑ e^x-1 ㈒ e+1/e-21162
4123
1163
11164
21165
21166
㈎ _< ㈏ _> ㈐ -e^y+1 ㈑ e^y-1 ㈒ e+1/e-21167
ln~31168
16/31169
11170
풀이 130쪽1171
4-3~ln~31172
8/31173
412 -23 -ln~21174
2e+2/e-41175
421176
4131177
⑴ -2~cos~t+2 ⑵ 131178
121179
5/41180
21181
12(e^2-1)1182
pai1183
14/31184
e-1/e1185
④1186
㈎ k/n ㈏ 1/31187
01188
14/31189
②1190
1/31191
⑤1192
③1193
e^31194
④1195
③1196
2~ln~4/31197
①1198
①1199
e+ 1e^2-11200
③1201 e^2-17/2e
1202
④1203
④1204
2~ln~21205
21/4-4~ln~21206
②1207
51208
⑴ y=1/ex ⑵ e/2-11209
64/91210
pai /21211
11212
④1213
1/61214
②1215
①1216
e+1/31217
⑴ 1/e ⑵ e^2-2e1218
215`cm^31219
②1220
681221
181222
51223
13 31224
①1225
51226
21227
④1228
②1229
2 3/1230
2(e-1/e)1231
②1232
31233
㈎ 1/n ㈏ n^4 ㈐ 1/41234
1-1/e1235
361236
3- 1e^21237
2(13 -1)1238
2201239
⑤1240
191241
e^32 -11242
①1243
100pai1244
①1245
⑤1246
15/4+ln~21247
③1248
③1249
③1250
21251
①0776
①0777
20/90778
③0779
②0780
②0781
y=ex-10782
-13 _<a_<130783
④0784
④0785
7/20786
20787
③0788
②0789
②0790
③0791
-20792
풀이 83쪽0793
풀이 83쪽0794
풀이 83쪽0795
풀이 83쪽0796
풀이 83쪽0797
(0, 1)0798
(0, 0), (3, 81)0799
(2, 2e^2 )0800
(-12 , ln~4), (12 , ln~4)0801 (pai/2, pai/2)
0802
㈎ 1 ㈏ 13 ㈐ 1/2 ㈑ 13 4 ㈒ y=00803
풀이 83쪽0804
풀이 84쪽0805
풀이 84쪽0806
풀이 84쪽0807
풀이 84쪽0808
최댓값: 1, 최솟값: -10809
최댓값: 412 , 최솟값: -4120810
최댓값: 9e^3, 최솟값: 00811
최댓값: 1e^2 +2, 최솟값: 10812
최댓값: pai/6+13 , 최솟값: 5/6pai-130813
풀이 85쪽0814
00815
10816
10817
10818
20819
㈎ 1- 1x/+1 ㈏ 0 ㈐ 00820
풀이 86쪽0821
풀이 86쪽0822
속도: -1/e, 가속도: 1/e0823
속도: 1, 가속도: -20824
속도: (4, 7), 가속도: (0, 2)0825
속도: (18, 13), 가속도: (6, 4)0826
속도: (9, 100), 가속도: (12, 108)0827
속도: ( 13 2 , -1/2), 가속도: (-1/2, - 13 2 )0828
속도: (1+ 13 2 , pai/3+1/2), 가속도: (-1/2, 2+ 13 2 )0829
속력: 12 , 가속도의 크기: 1/20830
속력: 22+2e^4x , 가속도의 크기: 12 e^20831
①0832
①0833
a_>20834
④0835
①0836
④0837
6~ln~20838
-30839
②0840
⑤0841
-9/8-ln~40842
a<60843
④0844
ㄱ, ㄷ0845
⑤0846
40847
①0848
⑤0849
280850
40851
②0852
40853
③0854
1/e0855
30856
⑤0857
-pai0858
②0859
-30860
③0861
320862
③0863
-1/e0864
⑤0865
1/e0866
3/40867
2pai- 2163 pai0868
10869
100870
⑤0871
k>27/40872
⑤0873
0_<k<10874
④0875
③0876
⑤0877
a<-10878
③0879
k_>-3/20880
-40881
③0882
-e<m_<00883
①0884
-40885
속도: 1/2, 가속도: 1/160886
①0887
③0888
50889
②0890
110q0891
(0, 2)0892
④0893
②0894
117q0895
③0896
②0897
- 41390898
0<k<1/40899
117q 20900
-80901 ③
0902
- 8e^20903
③0904
③0905
④0906
③0907
50908
20909
400910
④0911
80912
16 90913
③0914
⑤0915
8x^2~^32x^2w +C 3/0916
- 14x^4 +C0917
2/3x1x+C0918
4/5x~^41x+C0919
5/7~x~^52x^2w +C0920
-1/x+C0921
4~ln|x|+C0922
2/5x^21xq +C0923
1/2x^2- 12x^2 +C0924
ln|x|+1/x- 13x^3 +C0925
5~ln|x|+2/x+C0926
x+~ln|x|+ 2x^2+C0927
2/3x1xq +21xq +C0928
61x+ 21xq +C
0929
4/5x^21xq -21xq +C0930
3x1xq +x+C /20931
2/7x^31xq +4/5x^21xq +2/3x1xq +C0932
x-41xq +ln|x|+C0933
1/3x^3+1/x+C0934
2e^x+C0935
ex+3+C0936
4ln~4 +Cx+20937
25^xln~25 +C0938
4^xln~4 -2x+1
ln~2 +x+C
0939
e^x+x+C0940
x-2~sin~x+C0941
5~tan~x+C0942
-2~cos~x-sin~x+C0943
-cot~x+3/2x^2+C0944
tan~x+sec~x+C0945
-cos~x-4~cot~x+C0946
㈎ sec^2~x ㈏ tan~x0947
x+sin~x+C0948
-cos~x+C0949
-cot~x-x+C0950
㈎ t-1/3 ㈏ 1/3 ㈐ 1/180951
1/5(x+5)^5+C0952
- 13(3x+4) +C
0953
-1/4~sin~(2-4x)+C0954
5e/1 5x-1+C0955
2/5(x-1)^21x-1z +2/3(x-1)1x-1z +C0956
㈎ cos~x ㈏ t^2 ㈐ 1/30957
1/4(x^2-1)^4+C0958
2e^x1/ ^2+C0959
1/2(ln~x)^2+C0960
ln|x^2+5x-1|+C0961
-ln|cos~x|+C0962
x+ln|x+3|+C0963
1/2x^2-2x+ln|x+2|+C0964
ln| xx+1|+C
0965
ln| x-3x+3 |+C0966
⑴ a=1, b=2 ⑵ ln|(x+1)(x-1)^2|+C0967
㈎ cos~x ㈏ sin~x ㈐ sin~x ㈑ x~sin~x+cos~x0968
xe^x-e^x+C0969
x~ln~x-x+C0970
-(x+2)cos~x+sin~x+C0971
1/2x^2~ln~x-1/4x^2+C0972
⑤0973
1/3x^3-ln|x|+C0974
~f(x)=2/5x^21xq -x+20975
⑤0976
6-e^20977
④0978
③0979
③0980
20981
①0982
-20983
③0984
tan~x-sec~x+C0985
2pai /30986
①0987
10988
1/50989
20531
y'=2x~cot~x-x^2~csc^2~x0532
y'= 11+cos~x
0533
y'=20(5x-2)^30534
y'=4e^4^x0535
y'=33x+2~ln30536
y'=5~cos~5x0537
y'=-3~sin(3x+2)0538
y'=- 8(2x+3)^5
0539
y'=3(x+2/x)^^2(1- 2x^2 )0540
y'= 3x^2+2x^3+2x+10541
y'= 5(5x+2)ln~2
0542
y'=-tan~x0543
y'= e^xex+2
0544
y'= 121xq0545
y'=- 32x^21xq0546
y'=13 x13 -10547
y'= exe+10548
y'= 2x+122x^2+sx+1x
0549
y'=- x (x^2+3)2x^2+3x0550
dydx =6t^20551
dydx =t^2-12t^3
0552
dydx =( tt/+2)^^20553
dydx =e2t-1e2t+1
0554
dydx =-tan~t0555
dydx =-x/2y(ynot=0)0556
dydx =5/2y(ynot=0)0557
dydx =-y/x(xnot=0)0558
dydx =y/x0559
dydx =2x^3y (ynot=0)
0560
dydx =2xy0561
⑴ 1/5 ⑵ 1/140562
⑴ 1/2 ⑵ 3/40563
y''=12x^2+60564
y''=150(5x-1)0565
y''= 6x^2-6(x^2+3)^30566
y''=- 14(x-2)1x-2z
0567
y''=4e^2^x0568
y''=- 1(x+1)^2
0569
y''=-4~cos~2x0570
y''=-2~sin~x-x~cos~x0571
y''=2e^x~cos~x0572
1/40573
- 213 90574
②0575
-1/20576
③0577
④0578
60579
30580
e+1/80581
2 /310582
⑤0583
-250584
⑤0585
2120586
10587
③0588
2(e^2+e+1)0589
③0590
⑤0591
⑴ (2+3t)^3`cm^3 ⑵ 576`cm^3///s0592
④0593
2~ln~20594
③0595
40596
④0597
⑤0598
-pai/30599
-5/80600
①0601 ①
0602
3~ln~220603
-200604
③0605
③0606
20607
③0608
20609
-10610
-3/20611
②0612
11/40613
-12 /0614
③0615
dydx =x+1y-1 (ynot=1)0616
-1/pai0617
⑴ x^2+y^2=25 ⑵ dydx =-x/y~(ynot=0) ⑶ -3/40618
①0619
10 7/0620
e+1e0621
⑤0622
⑤0623
31240624
①0625
2-12 20626
③0627
②0628
1/e0629
20630
⑤0631
30632
①0633
30634
③0635
⑤0636
④0637
④0638
- 313 20639
50640
②0641
②0642
-39/160643
-10644
5/90645
①0646
①0647
ln~220648
①0649
30650
-10651
⑤0652
30653
①0654
②0655
1650656
①0657
120658
④0659
50660
①0661
pai/40662
y=-x+60663
y= 12 2 x+12 20664
y=e^2x0665
y=x+ln~3-10666
y=-13 x+ 13 6 pai+1/20667
y=-x+30668
y=x+10669
y=-x+10670
y=ex-20671
y=x0672
y=2ex0673
y=1/4x+7/40674
y=x-10675
풀이 66쪽0676
풀이 66쪽0677
풀이 66쪽0678
풀이 67쪽0679
풀이 67쪽0680
풀이 67쪽0681
풀이 67쪽0682
풀이 67쪽0683
풀이 67쪽0684
풀이 67쪽0685
풀이 67쪽0686
풀이 68쪽0687
풀이 68쪽0688
극솟값: 120689
극댓값: 1/4, 극솟값: -1/40690
극댓값: 10691
극솟값: 2-2~ln~20692
극댓값: pai/6+13 , 극솟값: 5/6pai-130693
풀이 68쪽0694
극댓값: 2, 극솟값: 10695
극솟값: -1/40696
극댓값: 1/2e0697
극솟값: ln~30698
극댓값: 120699
④0700
①0701 -3
0702
-10703
③0704
-30705
pai0706
③0707
20708
②0709
60710
y=1/2x+5/40711
③0712
③0713
-30714
61550715
③0716
-1/30717
y=x+10718
pai/20719
④0720
①0721
①0722
31550723
- 4e^20724
20725
②0726
a<-16 또는 a>160727
②0728
e^240729
32/50730
②0731
-1/30732
⑤0733
-5/40734
②0735
20736
-50737
①0738
③0739
10740
①0741
③0742
90743
a_<-30744
③0745
40746
③0747
40748
1520749
②0750
e/30751
20752
④0753
-10754
y=x0755
③0756
③0757
-e2pai0758
-10759
③0760
③0761
2e0762
-1_<k_<10763
a_>00764
①0765
②0766
30767
0<a<10768
①0769
20770
⑤0771
③0772
00773
pai/30774
e^2+e+10775
①219 라이트센미적분빠른정답찾기_ok.indd 2 18. 8. 29. 오후 4:45