Problem 465E: For the following exercises, show that F(x) are antiderivatives of f(x). 465.... Problem 466E: For the following exercises, show that F(x) are antiderivatives of f(x). 466. F(x)=x2+4x+1,f(x)=2x+4 Problem 467E: For the following exercises, show that F(x) are antiderivatives of f(x) . 467.... Problem 468E: For the following exercises, show that F(x) are antiderivatives of f(x) . 468. F(x)=cosx,f(x)=sinx Problem 469E: For the following exercises, show that F(x) are antiderivatives of f(x) . 469. F(x)=ex,f(x)=ex Problem 470E: For the following exercises, find the antiderivative of the function. 470. f(x)=1x2+x Problem 471E: For the following exercises, find the antiderivative of the function. 471. f(x)=ex3x2+sinx Problem 472E: For the following exercises, find the antiderivative of the function. 472. f(x)=ex+3xx2 Problem 473E: For the following exercises, find the antiderivative of the function. 473. f(x)=x1+4sin(2x) Problem 474E: For die following exercises, find the antiderivative F(x) of each function f(x). 474. f(x)=5x4+4x5 Problem 475E: For the following exercises, find the antiderivative F(x) of each function f(x). 475. f(x)=x+12x2 Problem 476E: For the following exercises, find the antiderivative F(x) of each function f(x). 476. f(x)=1x Problem 477E: For the following exercises, find the antiderivative F(x) of each function f(x). 477. f(x)=(3)3 Problem 478E: For the following exercises, find the antiderivative F(x) of each function f(x). 478.... Problem 479E: For the following exercises, find the antiderivative F(x) of each function f(x). 479. f(x)=x1/3x2/3 Problem 480E: For the following exercises, find the antiderivative F(x) of each function f(x). 480.... Problem 481E: For the following exercises, find the antiderivative F(x) of each function f(x). 481. f(x)=sec2(x)+1 Problem 482E: For the following exercises, find the antiderivative F(x) of each function f(x). 482. f(x)=sinxcosx Problem 483E: For the following exercises, find the antiderivative F(x) of each function f(x). 483.... Problem 484E: For the following exercises, find the antiderivative F(x) of each function f(x). 484. f(x)=0 Problem 485E: For the following exercises, find the antiderivative F(x) of each function f(x). 485.... Problem 486E: For the following exercises, find the antiderivative F(x) of each function f(x). 486.... Problem 487E: For the following exercises, find the antiderivative F(x) of each function f(x). 487.... Problem 488E: For the following exercises, find the antiderivative F(x) of each function f(x). 488.... Problem 489E: For the following exercises, find the antiderivative F(x) of each function f(x). 489.... Problem 490E: For the following exercises, evaluate the integral. 490. (1)dx Problem 491E: For the following exercises, evaluate the integral. 491. sinxdx Problem 492E: For the following exercises, evaluate the integral 492. (4x+ x)dx Problem 493E: For the following exercises, evaluate the integral. 493. 3 x 2+2 x 2dx Problem 494E: For the following exercises, evaluate the integral. 494. (secxtanx+4x)dx Problem 495E: For the following exercises, evaluate the integral. 495. (4 x+ x 4)dx Problem 496E: For the following exercises, evaluate the integral. 496. ( x 1/3 x 2/3 )dx Problem 497E: For the following exercises, evaluate the integral. 497. 14 x 3+2x+1 x 3dx Problem 498E: For the following exercises, evaluate the integral. 498. ( e x+ e x)dx Problem 499E: For the following exercises, solve the initial value problem. 499. f(x)=x3,f(1)=1 Problem 500E: For the following exercises, solve the initial value problem 500. f(x)=x+x2,f(0)=2 Problem 501E: For the following exercises, solve the initial value problem. 501. f(x)=cosx+sec2(x),f(4)=2+22 Problem 502E: For the following exercises, solve the initial value problem. 502. f(x)=x38x2+16x+1,f(0)=0 Problem 503E: For the following exercises, solve the initial value problem. 503. f(x)=2x2x22,f(1)=0 Problem 504E: For the following exercises, find two possible functions f given the second-or third-order... Problem 505E: For the following exercises, find two possible functions f given the second-or third-order... Problem 506E: For the following exercises, find two possible functions f given the second-or third-order... Problem 507E: For the following exercises, find two possible functions f given the second-or third-order... Problem 508E: For the following exercises, find two possible functions f given the second-or third-order... Problem 509E: A car is being driven at a rate of 40 mph when the brakes are applied. The car decelerates at a... Problem 510E: In the preceding problem, calculate how far the car travels in the time it takes to stop. Problem 511E: You are merging onto the freeway, accelerating at a constant rate of 12 ft/sec2. How long does it... Problem 512E: Based on the previous problem, how far does the car travel to reach merging speed? Problem 513E: A car company wants to ensure its newest model can stop in 8 sec when traveling at 75 mph. If we... Problem 514E: A car company wants to ensure its newest model can stop in less than 450 ft when traveling at 60... Problem 515E: For the following exercises, find the antiderivative of the function, assuming F(0)=0 . 515. [T]... Problem 516E: For the following exercises, find the antiderivative of the function, assuming F(0)=0 . 516. [T]... Problem 517E: For the following exercises, find the antiderivative of the function, assuming F(0)=0 . 517. [T]... Problem 518E: For the following exercises, find the antiderivative of the function, assuming F(0)=0 . 518.[T]... Problem 519E: For the following exercises, find the antiderivative of the function, assuming F(0)=0 . 519. [T]... Problem 520E: For the following exercises, find the antiderivative of the function, assuming F(0)=0 . 520. [T]... Problem 521E: For the following exercises, determine whether the statement is true or false. Either prove it is... Problem 522E: For the following exercises, determine whether the statement is true or false. Either prove it is... Problem 523E: For the following exercises, determine whether the statement is true or false. Either prove it is... Problem 524E: For the following exercises, determine whether the statement is true or false. Either prove it is... format_list_bulleted