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mathematics
calculus 6th edition

Questions and Answers of Calculus 6th edition

Evaluate the integral. 10 (x - 1)(x² + 9) dx
Evaluate the integral.∫x sin x cos x dx
Evaluate the integral. S X x² + x + 1 x2 dx
Evaluate the integral. 3x² - 2 √x²² - 2x - 8 dx
Evaluate the integral. y So y dy 2y e
Evaluate the integral.∫sec6t dt
Evaluate the integral. 3x³x² + 6x - 4 (x² + 1)(x² + 2) - dx
Evaluate the integral. x² = x + 6 x³ + 3x dx
Evaluate the integral. S dt t² - 6t + 13
Evaluate the integral.∫(tan2x + tan4x) dx
Evaluate the integral.∫ In(x2 - 1) dx
Evaluate the integral. Ső x³ cos x dx
Evaluate the integral.∫ex cos x dx
Use the guidelines of this section to sketch the curve.y = x√5 – xData from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y =
Use the guidelines of Section 4.5 to sketch the curve.y = x3 – 6x2 – 15x + 4 Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a
Use Newton’s method to find all roots of the equation correct to six decimal places.1/x = 1 + x3
Find the most general antiderivative of the function. (Check your answer by differentiation.)f(x) = 2 + x2/1 + x2
Use the guidelines of Section 4.5 to sketch the curve.y = x4 – 3x3 + 3x2 – xData from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a
Use the guidelines of this section to sketch the curve.y = √x2 + x – xData from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y
Use the guidelines of Section 4.5 to sketch the curve.y = 1/1 – x2Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y = f(x)
Use the guidelines of this section to sketch the curve.y = e2x – exData from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y =
Use a computer algebra system to graph f and to find f' and f". Use graphs of these derivatives to estimate the intervals of increase and decrease, extreme values, intervals of concavity, and
Use Newton’s method to find all roots of the equation correct to six decimal places.cos x = √x
Use the guidelines of this section to sketch the curve.y = ex/xData from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y = f(x) by
Use the guidelines of this section to sketch the curve.y = 1/(1+ e–x)Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y =
Use Newton’s method to find all roots of the equation correct to six decimal places.tan x = √1 – x2
Use the guidelines of this section to sketch the curve.y = ln(x2 – 3x + 2)Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve
Use the guidelines of this section to sketch the curve.y = x – ln xData from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y =
Use the guidelines of this section to sketch the curve.y = xe–x2Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y = f(x)
Use the guidelines of this section to sketch the curve.y = (x2 – 3) e–xData from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y
Use the guidelines of this section to sketch the curve.y = e3x + e–2xData from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y =
Find f.f"(x) = 2 + cos x, f(0) = –1, f(π/2) = 0
Use the guidelines of this section to sketch the curve. In guideline D find an equation of the slant asymptote.y = –2x2 + 5x – 1/2x – 1Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The
Use the guidelines of this section to sketch the curve.y = tan–1(x – 1/x + 1)Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a
Find f.f"(t) = 2et + 3 sin t. f(0) = 0, f(π) = 0
Find f.f"(x) = x–2, x > 0, f(1) = 0, f(2) = 0
Find f.f"'(x) = cos x, f(0) = 1, f'(0) = 2, f"(0) = 3
Evaluate the integral. Jo 10* dx
Evaluate the integral. 7/3 π/4 sec Ꮎ tan Ꮎ dᎾ
Evaluate the integral. √√3/2 6 √1/²² √1-1² = dt J1/2
Evaluate the integral. ᎾᏢ - dᎾ Jo 0-S00 0-500 + [ v/=
Evaluate the integral. 4 Jo t² + 1 dt
Evaluate the integral. #/3 sin + sin 0 tan²0 10 sec²0 de
Evaluate the integral. e²+1 du
Evaluate the integral. 64 J1 1 + √√x √x - dx
Evaluate the integral. *10 2e* |−10 sinh x + cosh x dx
Evaluate the integral. 2 4 + u² 3 J1 n np.
Evaluate the integral. f(x) dx where f(x). R sin x cosx if 0
Evaluate 2 sin x cos*x dx.
Evaluate the integral. 1/√3 1² - 1 t-1 - dt
Given thatwhat is (²3x√√x² + 4 dx = 5√5 - 8,
Evaluate the integral. f(x) dx where f(x) = if -2 ≤ x ≤0 4- x² if 0
Evaluate the integral. J1 (x - 1)³ -dx 2 x²
Evaluate the integral. S²₁ (x - 2)x) dx -1
Find the derivative of the function. F(x) = f'₁² ₁ = [₁ √t + sint dt x
Evaluate the integral. *3π/2 Jo | sin x | dx
Find the derivative of the function. g(x)= sin x 1-² 1+,4 ܟ dt
Find the derivative of the function. ===²=² - dt t y=
Find the derivative of the function. (3x+1 y= = J2x sin(t¹) dt
Find the derivative of the function. g(x) 1 - Stoms √2 + 1² tan..x dt
Find the derivative of the function. y-f √t sin t dt
If wherefind f"(2). F(x) = f(t) dt. 1
Find the derivative of the function. y = - 5x cos.x cos(u²) du
Find the interval on which the curveis concave upward. 1 Jo 1 + 1 + 1² y=√₁₁ = y dt
Evaluate 9 9 9 n - [☺) - () + ()* - - - (;)] lim + + 71 n n n
Find the area of the shaded region. у У y=5r-r y=x ((4,4) X
How much work is done in lifting a 40-kg sandbag to a height of 1.5 m?
Find the average value of the function on the given interval.f(x) = 4x – x2, [0, 4]
Find the area of the shaded region. y y= √√√x+2 y = x= x = 2 1 x+1 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 = 2 – 1/2x, y = 0, x
Find the work done if a constant force of 100 lb is used to pull a cart a distance of 200 ft.
Find the average value of the function on the given interval.f(x) = sin 4x, [–π, π]
Find the area of the shaded region. x=y²-2 у=-1 У y=1 x=ey ➜ X
Find the area of the region bounded by the given curves.y = 1/x, y = x2, y = 0, x = e
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 = 1 – x2, y = 0;
Find the average value of the function on the given interval.g(x) = 3√x. [1,8]
Find the area of the shaded region. (-3,3)- У x = y² - 4y x=2y-y² 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 = 1/x, x = 1, x = 2, y
Find the average value of the function on the given interval.g(x) = x2√1 + x3, [0.2]
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 = √25 - x2, y = 0, x
Find the average value of the function on the given interval.f(t) = te–t2 , [0, 5]
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 = 2√y, x = 0, y = 9;
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 average value of the function on the given interval.f(θ) = sec2(θ/2), [0, π/2]
Find the area of the region bounded by the given curves.y = √x, y = x2, x = 2
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 = ln x, y = 1, y = 2, 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
Find the average value of the function on the given interval.h(x) = cos4x sinx, [0, π]
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 = x3, y = x, x ≥ 0;
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 average value of the function on the given interval.h(u) = (3 – 2u)–1, [–1,1]
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 = 1/4x2, y = 5 – x2;
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
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.y = 1/4x2, x = 2, y = 0;
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 y
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.y = e–x, y = 1, x = 2;
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.ky = 1/x, y = 0, x = 1, x

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