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mathematics
calculus 6th edition

Questions and Answers of Calculus 6th edition

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.x = y2, x = 1; about x = 1
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.y = x, y = √x; about x
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.y = x2, x = y2; about x =
Refer to the figure and find the volume generated by rotating the given region about the specified line. R1 about OA y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1,1) A(1,0) X
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.y = x, y = 0, x = 2, x =
Refer to the figure and find the volume generated by rotating the given region about the specified line. R1 about BC y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1, 1) A(1,0) X
Refer to the figure and find the volume generated by rotating the given region about the specified line. R1 about AB y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1, 1) A(1,0) X
Refer to the figure and find the volume generated by rotating the given region about the specified line. R2 about OA y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1,1) A(1,0) X
Refer to the figure and find the volume generated by rotating the given region about the specified line. R2 about OC y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1, 1) A(1,0) X
Refer to the figure and find the volume generated by rotating the given region about the specified line. R2 about AB y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1, 1) A(1,0) X
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the
Refer to the figure and find the volume generated by rotating the given region about the specified line. R2 about BC y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1, 1) A(1,0) X
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the
Refer to the figure and find the volume generated by rotating the given region about the specified line. R3 about OA y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1,1) A(1,0) X
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the
Refer to the figure and find the volume generated by rotating the given region about the specified line. R3 about OC y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1,1) A(1,0) X
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the
Refer to the figure and find the volume generated by rotating the given region about the specified line. R3 about AB y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1, 1) A(1,0) X
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the
Refer to the figure and find the volume generated by rotating the given region about the specified line. R3 about BC y. C(0, 1) 0 R₂ y=√√√x R3 R₁ y=x³ B(1, 1) A(1,0) X
Use calculus to find the area of the triangle with the given vertices.(0,5), (2, –2), (5,1)
Use a graph to estimate the -coordinates of the points of intersection of the given curves. Then use this information and your calculator to estimate the volume of the solid obtained by rotating
Evaluate the integral. 17 - 2x² x² -dx; entry 33
Use a graph to find approximate -coordinates of the points of intersection of the given curves. Then find (approximately) the area of the region bounded by the curves. y = ex, y = 2 – x2
Evaluate the integral. (5 X Jo x + 10 - dx
Use a graph to find approximate -coordinates of the points of intersection of the given curves. Then use your calculator to find (approximately) the volume of the solid obtained by rotating about the
Use a graph to find approximate -coordinates of the points of intersection of the given curves. Then find (approximately) the area of the region bounded by the curves. y = x cos x, y = x10
Evaluate the integral. 3x √3 - 2x -dx; entry 55
Evaluate the integral.∫sin3x cos2x dx
Evaluate the integral. 3 sin ³x COS X dx
Evaluate the integral using integration by parts with the indicated choices of u and dv.∫θ cos θ dθ; u = θ, dv = cos θ dθ
Evaluate the integral.∫sin6x cos3x dx
Evaluate the integral. (5 Jo ,-0.6y ye dy
Evaluate the integral. se sec³(x) dx; entry 71
Evaluate the integral. sin x + sec x tan x - dx
Evaluate the integral. 3/4 sin³x cos³x dx TT/2
Evaluate the integral.∫x cos 5x dx
Evaluate the integral. #/2 cos ( So 1 + sin e de 0
Evaluate f² (√/1 − x² − √/1 − x³) dx. -
Evaluate the integral. (2√3 1²√³√16 - x² X-3 0 dx
Evaluate the integral. e20 sin 30 d0; entry 98
Evaluate the integral.∫xe–x dx
Evaluate the integral. TT/2 cos³x dx
Evaluate the integral. St dt (2t + 1)³
Evaluate the integral.∫tan3θ dθ
Evaluate the integral. 2 1/2 1 1³√1²-1 - dt
Evaluate the integral. 2t So (7-3)²" (t dt
Evaluate the integral.∫rer/2 dr
Evaluate the integral. *#7/2 Jo sin³ 0 cos²0 de
Evaluate the integral. IC .2 √√√x² - 1 dx x
Evaluate the integral.∫sin2 (πx) cos5 (πx) dx
Evaluate the integral. X 3-x4 dx
Evaluate the integral.∫t sin 2t dt
Evaluate the integral. 1 y²-4y - 12 dy
Evaluate the integral. sin³ (√x) dx X)
Evaluate the integral. √x = 69 - dx
Evaluate the integral. 1 x²√25-x² - x² dx
Evaluate the integral. arctan y 5²₁ dy −11+ y²
Evaluate the integral.∫x2 sin π x dx
Evaluate the integral. 1 12x - dx
Evaluate the integral. *8 * √x dx
Evaluate the integral. L°₂ (u² − u² + u²) du
Evaluate the integral. $2²3, dr dt
Evaluate the integral. -2 (3u + 1)² du
Evaluate the integral. *2π 4 cos e de
Evaluate the integral. (2v + 5)(3v1) dv
Evaluate the integral. ² x(2 + x³) dx
Prove that fx dx = b² − a² 2
Evaluate the integral. √t (1 + t) dt
Evaluate the integral. f² (3 + x√x) dx Jo
Prove that b³ - a³ f₁ x² dx = 5² 3 D
Evaluate the integral. S√Zt dt 21 10
Evaluate the integral. p T-X6J
Evaluate the integral. 2 [² ( 49² + ²/3) a dy ,3
Evaluate the integral. f(y − 1)(2y + 1) dy Jo
Evaluate the integral. ² y + 5y² ,3 J1 dy
Evaluate the integral. 1/4 sec²t dt
Evaluate the integral. fx (√x + √x) dx
Evaluate the integral. *π/4 Jo sec 0 tan 0 de
Evaluate the integral. S³ (2e² + 4 cos x) dx
Evaluate the integral. f² (1 + 2y)² dy J1
Evaluate the integral. 5 X dx
Evaluate the integral. cosh t dt
Evaluate the integral. 3x - 2 1.³ ³. X -dx
Evaluate the integral. Jo (4 sin 0 - 3 cos 0) de
Use the guidelines of this section to sketch the curve. In guideline D find an equation of the slant asymptote.y = x2 + 12/x – 2Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following
Use the guidelines of this section to sketch the curve. In guideline D find an equation of the slant asymptote.xy = x2 + 4Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following
Use the guidelines of this section to sketch the curve. In guideline D find an equation of the slant asymptote.y = ex – xData from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following
Use the guidelines of this section to sketch the curve. In guideline D find an equation of the slant asymptote.y = 2x3 + x2 + 1/x2 + 1Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The
Find f.f'(x) = cos x – (1 – x2)–1/2
Use the guidelines of this section to sketch the curve. In guideline D find an equation of the slant asymptote.y = (x + 1)3/(x – 1)2Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The
Find f.f'(x) = 2ex + sec x tan x
Find f.f'(x) = √x3 + 3√x2
Find f.f'(x)= sinh x + 2 cosh x, f(0) = 2
Find f.f'(u) = u2 + √u/u, f(1) = 3
Find f.f"(x) = 1 − 6x + 48x2, f(0) = 1, f'(0) = 2
Find f.f"(x) = 2x3 + 3x2 – 4x + 5, f(0) = 2, f(1) = 0
Find the minimum value of the area of the region under the curve y = x + 1/x from x = a to x = a + 1.5, for all a > 0.
If f is a differentiable function such that f(x) is never 0 andfor all x, find f. f(t)dt = [f(x)]²

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