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mathematics
calculus 6th edition

Questions and Answers of Calculus 6th edition

(a) Find the Riemann sum for f(x) = sin x, 0 ≤ x ≤ 3π/2, with six terms, taking the sample points to be right endpoints. (Give your answer correct to six decimal places.) Explain what the
If where find f'(π/2). f(x) g(x) Jo 0 1 √1 + 1³ =dt
Evaluate - lim 1 f* (1 – tan 2t)¹/¹ dt. - x0 x Jo
Evaluate: (a) O 1 d Jo dx ·$· d x arctan. ^x) dx dx Jo - 15. ,arctan t e dt (b) dx Jo , arctanx dx
Find d² dx² - S² (1 "sin f √1 + ut du dt.
Evaluate lim 1 √n√√√n+1 + 1 √√√√√n + 2 + + 1 [n√n+n
Evaluate the integral. 5 ₂6 dx
Evaluate the integral. 2² (6x² - 4x + 5) dx
Evaluate the integral. J (1 + u* -u³) du
Evaluate the integral. ²³ (1 + 2x - 4x³) dx
Evaluate the integral. So x4/5 dx
Evaluate the integral. ro L₁ (2x - e¹) dx
Use Newton’s method to approximate the indicated root of the equation correct to six decimal places.The root of 2.2x5 – 4.4x3 + 1.3x2 – 0.9x – 4.0 = 0 in the interval [–2, –1]
Use the guidelines of this section to sketch the curve.y = 2√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 this section to sketch the curve.y = √x2 + x – 2Data 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 = x/√x2 + 1Data 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 the roots of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations.x6 – x5 – 6x4 – x2 + x + 10 = 0
Use the guidelines of Section 4.5 to sketch the curve.y = x2/(x + 8)Data 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 = x/√x2 – 1Data 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) = 6x + 12x2
Use the guidelines of this section to sketch the curve.y = x – 3x1/3Data 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 + x3 + x6
Use the guidelines of Section 4.5 to sketch the curve.y = 3√x2 + 1Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y = f(x)
Find f.f"(x) = 2/3x2/3
Use the guidelines of Section 4.5 to sketch the curve.y = sin2x – 2 cos xData 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) = 6x + sin x
Use the guidelines of Section 4.5 to sketch the curve.y = x√2 + 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)
Use the guidelines of this section to sketch the curve.y = 3 sin x – sin3xData from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve
Use Newton’s method to find all the roots of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations.4e–x2 sin x = x2 – x + 1
Find f.f'"(t) = et
Use Newton’s method to find all the roots of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations.earctan x = √x3 + 1
Use the guidelines of Section 4.5 to sketch the curve.y = xe–2x Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y = f(x)
Find f.f'"(t) = t – √t
Use the guidelines of this section to sketch the curve.y = 1/2 x – sin x, 0 Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a
Find f.f'(x) = 1 – 6x, f(0) = 8
Find f.f'(x) = 8x3 + 12x + 3, f(1) = 6
Find f.f'(x) = √x (6 + 5x), f(1) = 10
Find f.f'(x) = 2x – 3/x4, x > 0, f(1) = 3
Find f.f'(t) = 2 cos t + sec2t, –π/2 < t < π/2, f(π/3) = 4
Find f.f'(x) = (x2 – 1)/x, f(1) = 1/2 f(–1) = 0
Use the guidelines of this section to sketch the curve.y= sin x/1 + cos xData 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) = x–1/3, f(1) = 1, f(–1) = –1
Find f.f'(x) = 4/√1 – x2, f(1/2) = 1
Use the guidelines of this section to sketch the curve.y = esin 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
Find f.f"(x) = 24x2 + 2x + 10. f(1) = 5, f'(1) = –3
Find f.f"(x) = 4 – 6x – 40x3, f(0) = 2, f'(0) = 1
Find f.f"(t) = 3/√t, f(4) = 20, f'(4) = 7
Find f.f"(x) = 2 – 12x, f(0) = 9, f(2) = 15
Find f.f"(x) = 20x3 + 12x2 + 4, f(0) = 8, f(1) = 5
Find the most general antiderivative of the function. (Check your answer by differentiation.)f(x) = 3ex + 7 sec2x
Use Newton’s method to approximate the indicated root of the equation correct to six decimal places.The positive root of sin x = x2
Find the most general antiderivative of the function. (Check your answer by differentiation.)g(θ) = cos θ – 5 sin θ
Use the guidelines of this section to sketch the curve.y = x – 1/x2
Find the most general antiderivative of the function. (Check your answer by differentiation.)f(t) = sin t + 2 sinh t
Use the guidelines of this section to sketch the curve.y = 1 + 1/x + 1/x2
Use Newton’s method to find all roots of the equation correct to six decimal places.x4 = 1 + x
Find the most general antiderivative of the function. (Check your answer by differentiation.)f(x) = 5ex – 3 cosh x
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 the guidelines of this section to sketch the curve.y = x2/x2 + 3
Use Newton’s method to find all roots of the equation correct to six decimal places.ex = 3 – 2x
Find the most general antiderivative of the function. (Check your answer by differentiation.)f(x) = 2√x + 6 cos x
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 the guidelines of this section to sketch the curve.y = x/x3 – 1
Use Newton’s method to find all roots of the equation correct to six decimal places.(x – 2)2 = ln x
Find the most general antiderivative of the function. f(x) = x5 – x3 + 2x/x4
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
Find the local and absolute extreme values of the function on the given interval.f(x) = x3 – 6x2 + 9x + 1, [2, 4]
Find the most general antiderivative of the function. (Check your answer by differentiation.)f(x) = x – 3
Use the guidelines of this section to sketch the curve.y = x3 + x
Find the most general antiderivative of the function. (Check your answer by differentiation.)f(x) = 1/2x2 – 2x + 6
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f has an absolute minimum value at c, then
Find the local and absolute extreme values of the function on the given interval.f(x) = 3x – 4/x2 + 1 [–2, 2]
Find the most general antiderivative of the function.f(x) = 1/2 + 3/4 x2 – 4/5 x3
(a) State Fermat’s Theorem.(b) Define a critical number of f.
Find the local and absolute extreme values of the function on the given interval.f(x) = (x2 + 2x)3. [–2,1]
Find the most general antiderivative of the function. (Check your answer by differentiation.)f(x) = 8x9 – 3x6 + 12x3
Find the local and absolute extreme values of the function on the given interval.f(x) = x + sin 2x, [0, π]
Find the most general antiderivative of the function. (Check your answer by differentiation.)f(x) = (x + 1)(2x – 1)
Find the local and absolute extreme values of the function on the given interval.f(x) = (ln x)/x2, [1. 3]
Find the most general antiderivative of the function. (Check your answer by differentiation.)f(x) = x(2 – x)2
Evaluate the limit. tan 77X lim x→ ln(1 + x)
Find the most general antiderivative of the function. (Check your answer by differentiation.)f(x) = 5x1/4 – 7x3/4
Evaluate the limit. lim x-0 1 - cos x 2 x² + x
Find the most general antiderivative of the function. (Check your answer by differentiation.)f(x) = 2x + 3x1.7
Evaluate the limit. lim x-0 4x e - 1 - 4x X
Find the most general antiderivative of the function. (Check your answer by differentiation.)f(x) = 6√x – 6√x
Evaluate the limit. lim 4x e - 1 - 4x 1²
Find the most general antiderivative of the function. (Check your answer by differentiation.)f(x) = 4√x3 + 3√x4
Use Newton’s method to approximate the given number correct to eight decimal places.5√20
Evaluate the limit. lim x³ex 3 -x x-
Find the most general antiderivative of the function. (Check your answer by differentiation.)f(x) = 10/x9
Use Newton’s method to approximate the given number correct to eight decimal places.100√100
Evaluate the limit. lim x² ln x x-0+
Find the most general antiderivative of the function. (Check your answer by differentiation.)g(x) = 5 – 4x3 + 2x6/x6
Use Newton’s method to approximate the indicated root of the equation correct to six decimal places.The root of x4 – 2x3 + 5x2 – 6 = 0 in the interval [1, 2]
Evaluate the limit. lim X x-1 1 1 ln x
Evaluate the limit. lim (tan x) cos x x → (m/2)-
Find the most general antiderivative of the function. (Check your answer by differentiation.)f(u) = u4 + 3√u/u2
(a) Find the intervals on which f is increasing or decreasing.(b) Find the local maximum and minimum values of f.(c) Find the intervals of concavity and the inflection points.f(x) = 4x3 + 3x2 – 6x
(a) Find the intervals on which f is increasing or decreasing.(b) Find the local maximum and minimum values of f.(c) Find the intervals of concavity and the inflection points.f(x) = e2x + e–x

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