826
Answer Key
435 . 0.159, 3.146 437 . We need f to be twice continuously differentiable. 439 . x =0 441 . x =−1 443 . x =5.619 445 . x =−1.326 447 . There is no solution to the equation. 449 . It enters a cycle. 451 . 0 453 . −0.3513 455 . Newton: 11 iterations, secant: 16 iterations 457 . Newton: three iterations, secant: six iterations 459 . Newton: five iterations, secant: eight iterations 461 . E =4.071 463 . 4.394%
465 . F ′( x ) =15 x 2 +4 x +3 467 . F ′( x ) =2 xe x + x 2 e x 469 . F ′( x ) = e x 471 . F ( x ) = e x − x 3 −cos( x )+ C 473 . F ( x ) = x 2 2 − x −2cos(2 x )+ C 475 . F ( x ) = 1 2 x 2 +4 x 3 + C 477 . F ( x ) = 2 5 ( x ) 5 + C 479 . F ( x ) = 3 2 x 2/3 + C 481 . F ( x ) = x +tan( x )+ C 483 . F ( x ) = 1 3 sin 3 ( x )+ C 485 . F ( x ) = − 1 2 cot ( x )− 1 x + C 487 . F ( x ) =−sec x −4csc x + C 489 . F ( x ) = − 1 8 e −4 x −cos x + C
491 . −cos x + C 493 . 3 x − 2 x + C 495 . 8 3 x 3/2 + 4 5 497 . 14 x − 2 x − 1 2 x 2
x 5/4 + C
+ C
499 . f ( x ) = − 1 2 x 2 + 3 2 501 . f ( x ) = sin x +tan x +1 503 . f ( x ) = − 1 6 x 3 − 2 x + 13 6
505 . Answers may vary; one possible answer is f ( x ) = e − x 507 . Answers may vary; one possible answer is f ( x ) =−sin x
509 . 5.867 sec 511 . 7.333 sec 513 . 13.75 ft/sec 2
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