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E h 501. f'(x) = cosx + sec²(x), (4) = 2 + √2 (7

E h 501. f'(x) = cosx + sec²(x), (4) = 2 + √2 (7

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Please solve 501, thanks!
ns of Derivatives noo ow far Chapter 4/Applications of Derivatives 4.10 EXERCISES For the following exercises, show that F(x) are antiderivatives of f(x).o visblins s 465 F(x) = 5x²³ + 2x² + 3x + 1₁ f(x) 466. 467. F(x) = x² + 4x + 1₁ f(x) = 2x + 4 abbris schal +3x+1₁ f(x) = 15x² + 4x +3 den x) = 1 + x 470. f(x)= F(x) = x²³e², f(x) = e* (x² + 2x) 489. f(x) = 4x+sinx ad nadw do 04 468. F(x) = cosx, f(x) = -sinxr (1) For the following exercises, find the antiderivative of the For the following exercises, evaluate the integral. 469 F(x)= e, f(x) = ex ((x)) lo svbevisblinssit function. Monted 490. f(-1)dx 491. sinxdx al point 471. f(x) = e* - 3x² + sinx pol 472. f(x) = ex+3x-x² 473. f(x)=x-1+4 sin(2x) For the following exercises, find the antiderivative F(x) of each function f(x). 474. f(x) = 5x² + 4x5 475. f(x) = x + 12x² 476. f(x)=√x 477. f(x)=(√x)³ 478. f(x)= x1/3+ (2x) 1/3 479. f(x) = 273 1/3 480. f(x) = 2 sin(x) + sin(2x) 481. f(x) = sec² (x) + 1 432. f(x) = sin.xcos.x dar contimunus 483. 484. 485. f(x)=csc²(x) + f(x) = sin² (x)cos(x) f(x) = 0 486. f(x)=cscxcotx+3x 487. f(x) = 4cscxcotx-secxtanx 488. f(x)= 8 secx(secx-4 tanx) won saiad Shal salualus maldong gabi 492. (4x+√x)dx o Bris k 493. sign in t 497. maldong auoiving si ob (secxtanx+4x)dx 495. (4√x+x) dx 163 io fabom was an 494. (secxtanx +4 16 novlab to suley se bril noleslash tosteroo aandailos 497 496. (x-1/3-2/3) dx 809 LADY 113 Dà s6 bange goigrom down ste A. 18 el copa lowon swans of snow sqm A Al of Od misala 024 sadiq 498. (e* + e*)dx wh IT are For the following exercises, solve the initial value problem. 499. f'(x) = x-³, f(1) = 1 [TS2 500. f'(x)=√x+x², f(0) = 2 whether the Laut p 501. f'(x) = cosx + sec²(x), ƒ(4) = 2+12 17 12 502. f'(x) = x³ - 8x² + 16x +1, f(0) = 0
Transcribed Image Text:ns of Derivatives noo ow far Chapter 4/Applications of Derivatives 4.10 EXERCISES For the following exercises, show that F(x) are antiderivatives of f(x).o visblins s 465 F(x) = 5x²³ + 2x² + 3x + 1₁ f(x) 466. 467. F(x) = x² + 4x + 1₁ f(x) = 2x + 4 abbris schal +3x+1₁ f(x) = 15x² + 4x +3 den x) = 1 + x 470. f(x)= F(x) = x²³e², f(x) = e* (x² + 2x) 489. f(x) = 4x+sinx ad nadw do 04 468. F(x) = cosx, f(x) = -sinxr (1) For the following exercises, find the antiderivative of the For the following exercises, evaluate the integral. 469 F(x)= e, f(x) = ex ((x)) lo svbevisblinssit function. Monted 490. f(-1)dx 491. sinxdx al point 471. f(x) = e* - 3x² + sinx pol 472. f(x) = ex+3x-x² 473. f(x)=x-1+4 sin(2x) For the following exercises, find the antiderivative F(x) of each function f(x). 474. f(x) = 5x² + 4x5 475. f(x) = x + 12x² 476. f(x)=√x 477. f(x)=(√x)³ 478. f(x)= x1/3+ (2x) 1/3 479. f(x) = 273 1/3 480. f(x) = 2 sin(x) + sin(2x) 481. f(x) = sec² (x) + 1 432. f(x) = sin.xcos.x dar contimunus 483. 484. 485. f(x)=csc²(x) + f(x) = sin² (x)cos(x) f(x) = 0 486. f(x)=cscxcotx+3x 487. f(x) = 4cscxcotx-secxtanx 488. f(x)= 8 secx(secx-4 tanx) won saiad Shal salualus maldong gabi 492. (4x+√x)dx o Bris k 493. sign in t 497. maldong auoiving si ob (secxtanx+4x)dx 495. (4√x+x) dx 163 io fabom was an 494. (secxtanx +4 16 novlab to suley se bril noleslash tosteroo aandailos 497 496. (x-1/3-2/3) dx 809 LADY 113 Dà s6 bange goigrom down ste A. 18 el copa lowon swans of snow sqm A Al of Od misala 024 sadiq 498. (e* + e*)dx wh IT are For the following exercises, solve the initial value problem. 499. f'(x) = x-³, f(1) = 1 [TS2 500. f'(x)=√x+x², f(0) = 2 whether the Laut p 501. f'(x) = cosx + sec²(x), ƒ(4) = 2+12 17 12 502. f'(x) = x³ - 8x² + 16x +1, f(0) = 0
Expert Solution
Step 1

Given: f'x=cosx +sec2x ; fπ4=2+22.We need to solve the above initial value problem.Recall the formulas: ∫cosx dx=sinx+C                   ∫sec2x dx = tanx+Cin

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