1off exp; 2 3 off mcd; 4 5 6mrv_limit(e^x,x,infinity); 7 8 9infinity 10 11 12ex:=log(log(x)+log(log(x)))-log(log(x)); 13 14 15ex := - (log(log(x)) - log(log(log(x)) + log(x))) 16 17ex:=ex/(log(log(x)+log(log(log(x))))); 18 19 20ex := 21 22 -1 23 - (log(log(x)) - log(log(log(x)) + log(x)))*log(log(log(log(x))) + log(x)) 24 25ex:=ex*log(x); 26 27 28ex := - (log(log(x)) - log(log(log(x)) + log(x))) 29 30 -1 31 *log(log(log(log(x))) + log(x)) *log(x) 32 33 34mrv_limit(e^-x,x,infinity); 35 36 370 38 39 40mrv_limit(log(x),x,infinity); 41 42 43infinity 44 45 46mrv_limit(1/log(x),x,infinity); 47 48 490 50 51 52a:=e^(1/x-e^-x)-e^(1/x); 53 54 55 -1 - x 56 x - e 57a := e *(e - 1) 58 59a:=a/e^(-x); 60 61 62 -1 - x 63 x + x - e 64a := e *(e - 1) 65 66 67mrv_limit(a,x,infinity) ; 68 69 70-1 71 % all of these are correct 72mrv_limit(e^-x,x,infinity) ; 73 74 750 76 77mrv_limit(log(x),x,infinity) ; 78 79 80infinity 81 82mrv_limit(1/log(x),x,infinity) ; 83 84 850 86 87 88a:=e^(1/x-e^-x)-e^(1/x); 89 90 91 -1 - x 92 x - e 93a := e *(e - 1) 94 95a:=a/e^(-x); 96 97 98 -1 - x 99 x + x - e 100a := e *(e - 1) 101 102b:=e^x*(e^(1/x-e^-x)-e^(1/x)); 103 104 105 -1 - x 106 x + x - e 107b := e *(e - 1) 108 109 110%c:=e^x*(e^(1/x+e^(-x)+e^(-x^2))-e^(1/x-e^(-e^x))) 111maxi1({e^(-x^2)},{e^x}); 112 113 114 2 115 - x 116{e } 117 118 119cc:= e^(log(log(x+e^(log(x)*log(log(x)))))/log(log(log(e^x+x+log(x))))); 120 121 122 x -1 log(x) 123 log(log(log(log(x) + x + e ))) *log(log(log(x) + x)) 124cc := e 125 126 127b:=e^x*(e^(1/x-e^-x)-e^(1/x)); 128 129 130 -1 - x 131 x + x - e 132b := e *(e - 1) 133 134 135c:=e^x*(e^(1/x+e^(-x)+e^(-x^2))-e^(1/x-e^(-e^x))); 136 137 138 x 2 139 -1 - e - x - x 140 x + x - e e + e 141c := - e *(e - e ) 142 143 144e^(log(log(x+e^(log(x)*log(log(x)))))/(log(log(log(e^x+x+log(x)))))); 145 146 147 x -1 log(x) 148 log(log(log(log(x) + x + e ))) *log(log(log(x) + x)) 149e 150 151 152%% mrv_limit(ws,x,infinity); 153 154aa:=e^(e^(e^x)); 155 156 157 x 158 e 159 e 160aa := e 161 162bb:=e^(e^(e^(x-e^(-e^x)))); 163 164 165 x 166 - e 167 - e + x 168 e 169 e 170bb := e 171 172ex1:=(e^x)*(e^((1/x)-e^(-x))-e^(1/x)); 173 174 175 -1 - x 176 x + x - e 177ex1 := e *(e - 1) 178 % returns -1 correct 179 180ex2:=(e^x)*(e^((1/x)-e^(-x)-e^(-x^2))-e^((1/x)-e^(-e^x))); 181 182 183 x 2 184 -1 - e - x - x 185 x + x - e - e - e 186ex2 := - e *(e - e ) 187 % returns infinity 188 189ex3:=e^(e^(x-e^-x)/(1-1/x))-e^(e^x); 190 191 192 - x 193 x - e + x -1 -1 194 e - e *(x - 1) 195ex3 := - (e - e ) 196 % returns - infinity 197 198ex4:=e^(e^((e^x)/(1-1/x)))-e^(e^((e^x)/(1-1/x-(log(x))^(-log(x))))); 199 200 201 x - log(x) -1 -1 x -1 -1 202 - e *(log(x) + x - 1) - e *(x - 1) 203 e e 204ex4 := - (e - e ) 205 206 207ex5:=(e^(e^(e^(x+e^-x))))/(e^(e^(e^x))); 208 209 210 - x 211 e + x x 212 e e 213 e - e 214ex5 := e 215 216 217ex6:=(e^(e^(e^x)))/(e^(e^(e^(x-e^(-e^x))))); 218 219 220 x 221 - e 222 - e + x x 223 e e 224 - e + e 225ex6 := e 226 227 228ex7:=(e^(e^(e^x)))/(e^(e^(e^(x-e^(e^x))))); 229 230 231 x 232 e 233 - e + x x 234 e e 235 - e + e 236ex7 := e 237 238 239ex8:=(e^(e^x))/(e^(e^(x-e^(-e^(e^x))))); 240 241 242 x 243 e 244 - e 245 - e + x x 246 - e + e 247ex8 := e 248 249 250ex9:=((log(x)^2)*e^(sqrt(log(x))*((log(log(x)))^2)*e^((sqrt(log(log(x))))*(log(log(log(x)))^3))))/sqrt(x); 251 252 253ex9 := 254 255 3 256 sqrt(log(log(x)))*log(log(log(x))) 2 257 - 1/2 e *sqrt(log(x))*log(log(x)) 2 258x *e *log(x) 259 260 261ex10:=((x*log(x))*(log(x*e^x-x^2))^2)/(log(log(x^2+2*e^(3*x^3*log(x))))); 262 263 264 3 265 3*x 2 -1 x 2 266ex10 := log(log(2*x + x )) *log((e - x)*x) *log(x)*x 267 268 269misc1:=1/(e^(-x+e^-x))-e^x; 270 271 272 - x 273 x - e 274misc1 := e *(e - 1) 275 % returns -1 correct 276 277misc2:=(e^(1/x-e^-x)-e^(1/x))/(e^-x); 278 279 280 -1 - x 281 x + x - e 282misc2 := e *(e - 1) 283 % returns -1 correct 284 285misc3:=e^(-log(x+e^-x)); 286 287 288 - x -1 289misc3 := (e + x) 290 % returns 0 correct 291 292misc4:=e^(x-e^x); 293 294 295 x 296 - e + x 297misc4 := e 298 % returns 0 correct 299 300% bb limit is infinity correct 301 302mrv_limit(ex,x,infinity); 303 304 3051 306 %1 307 308mrv_limit(ex1,x,infinity); 309 310 311-1 312 % -1 313 314%% mrv_limit(ex2,x,infinity); % -1 315 316%% mrv_limit(b,x,infinity); % -1 317 318mrv_limit(a,x,infinity); 319 320 321 - infinity 322 323 324%% mrv_limit(ex3,x,infinity); 325 326%% mrv_limit(ex4,x,infinity); 327 328%% mrv_limit(ex5,x,infinity); % 0 329 330%% mrv_limit(ex6,x,infinity); 331 332mrv_limit(misc1,x,infinity); 333 334 335-1 336 337 338mrv_limit(misc2,x,infinity); 339 340 341 - infinity 342 343 344mrv_limit(misc3,x,infinity); 345 346 3470 348 349 350mrv_limit(misc4,x,infinity); 351 352 3530 354 355 356end; 357 358Tested on x86_64-pc-windows CSL 359Time (counter 1): 172 ms plus GC time: 15 ms 360 361End of Lisp run after 0.17+0.07 seconds 362real 0.40 363user 0.04 364sys 0.03 365