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study help
mathematics
calculus 6th edition
Calculus 6th Edition James Stewart - Solutions
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 = f(x) by hand. Not every item is relevant to every function. (For instance, a given curve might not
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 = f(x) by hand. Not every item is relevant to every function. (For instance, a given curve might not
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 = f(x) by hand. Not every item is relevant to every function. (For instance, a given curve might not
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) by hand. Not every item is relevant to every function. (For instance, a given curve might not have
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 = f(x) by hand. Not every item is relevant to every function. (For instance, a given curve might not
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 = f(x) by hand. Not every item is relevant to every function. (For instance, a given curve might not
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) by hand. Not every item is relevant to every function. (For instance, a given curve might not have
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 = f(x) by hand. Not every item is relevant to every function. (For instance, a given curve might
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) by hand. Not every item is relevant to every function. (For instance, a given curve might not have
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 y = f(x) by hand. Not every item is relevant to every function. (For instance, a given curve might
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) by hand. Not every item is relevant to every function. (For instance, a given curve might not have
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 curve y = f(x) by hand. Not every item is relevant to every function. (For instance, a given curve might
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 = f(x) by hand. Not every item is relevant to every function. (For instance, a given curve might not
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 hand. Not every item is relevant to every function. (For instance, a given curve might not have
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 inflection points of f.f(x) = √x/x2 + x + 1
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 inflection points of f.f(x) = x2/3/1 + x + x4
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 inflection points of f.f(x) = √x + 5 sin x, x ≤ 20
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 f'(c) = 0.
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 + 1
(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
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem.f(x) = 5 – 12x + 3x2, [1,3]
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem.f(x) = x3 – x2 – 6x + 2, [0,3]
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