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Calculus: Early Transcendentals (3rd Edition)
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- √3 (tan−¹ (x)) (1 + x²)arrow_forwardsin(x) L²₁(x² - 4x² + 3x)2 Jax-0 |dx=0 1 (1+x²)² (A) True B) Falsearrow_forwardLet f(x) = 3× + 3, x, = 2, x2 and Ax = 1 4 (a) Find f(x) Ax b) The sum in part (a) approximates a definite integral using rectangles. The height of each rectangle is given by the value of the function at the left endpoint. Write the definite integral that the sum approximates. 4 (a) Ef(x) Ax: i= 1 (Simplify your answer.) (b) Find the definite integral that is approximated by the sum in part a. 4 Ef(x) Ax = ] O dx j=1arrow_forward
- Consider the indefinite integral ∫ (cos 2x)/(√sin 2x) dxdx.(a) Indicate the substitution u = u(x) you use and write the given integral as∫f(u) du. (b) Evaluate the integral from part (a), and use this to evaluate the originalindefinite integral. Write the answer in terms of a function of xarrow_forwarddx x*+3x +1)[tan (x1)]arrow_forwardf(x) = sin x In(5x)arrow_forward
- Consider the functions: h(x) = f(g(x)) and Use the graphs of f(x) and g(x) to find the following • h'(1) n'(x) = f'(gas)• g'(x) • h'(8) 10 8 6 2 CO g H H>X -2 12 4 6 8 10arrow_forwardIf b) 1 1 [ f(x)dx = ln(|x) - tan(x) - 4e* + then find f(x). ²+ + 6x + Carrow_forwardlim x→0 tan-¹ (8x) - 8x cos (8x) — 256x³3 - x5arrow_forward
- e-√2x e-V2x sinh x sin x x 80 dxarrow_forwarda) Find a function f so that f’(x) = 6x + cos(x). b) Find a function g with g’(x) = f’(x)arrow_forwardLet f(x)= (a) Compute the derivative of f. f'(x) = Añ ab PW b ab -3x²-71 b √a P |a| (b) Find the indefinite integral of f. Use capital letter C as the constant of integration. [ f(x) dx = k √a |a| sin (a) k E sin (a)arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning