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mathematics
calculus 6th edition

Questions and Answers of Calculus 6th edition

Suppose that f(1) = 2, (4) = 7, f'(1) = 5. f'(4) = 3, and f" is continuous. Find the value of fxf"(x) dx.
Evaluate the integral. S 1 √x+1+√√√x xp.
Evaluate the integral. *3 2 3 u³ + 1 3 u³ − u² du
Evaluate the integral. 3√1 + x² x² -dx
Evaluate the integral. 1 1 + 2e* - dx e*
Evaluate the integral. e2x 1 + e* -dx
Evaluate the integral. In(x + 1) dx 2 x²
Evaluate the integral. x + arcsin x dx √1-x²
Evaluate the integral. 4* + 10* 2* dx
Evaluate the integral. 1 (x - 2)(x² + 4) dx
Evaluate the integral. dx √x (2 + √x)* -S |)ª^
Show that So° x ²³e²x³² dx = of = Sex²¹dx.
Evaluate the integral. xe* √1 + e* dx
Find the centroid of the region bounded by the given curves.x = 5 – y2, x = 0
Find dy/dx.x = 1/t y = √te–t
Identify the type of conic section whose equation is given and find the vertices and foci.y2 + 2y = 4x2 + 3
Sketch the curve with the given polar equation.r2 – 3r + 2 = 0
Identify the type of conic section whose equation is given and find the vertices and foci.4x2 + 4x + y2 = 0
Find all points of intersection of the given curves.r = 1 + sinθ r = 3sinθ
Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.x = t – t2, y = 4/3t3/2, 1 ≤ t ≤ 2
Sketch the curve with the given polar equation.r = cos 5θ
Find an equation for the conic that satisfies the given conditions.Ellipse, foci (0, ±5), vertices (0, ±13)
Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.x = 1 + et, y = t2, –3 ≤ t ≤ 3
Sketch the curve with the given polar equation.r = 2cos 4θ
Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.x = t + cos t, y = t – sin t, 0 ≤ t ≤ 2π
Sketch the curve with the given polar equation.r = 3 cos 6θ
Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.x = ln t, y = √t + 1, 1 ≤ t ≤ 5
Sketch the curve with the given polar equation.r = 1 – 2 sin θ
Sketch the curve with the given polar equation.r = 2 + sinθ
Find the exact length of the curve.x = et + e–t, y = 5 – 2t, 0 ≤ t ≤ 3
Sketch the curve with the given polar equation.r2 = 9 sin 2θ
Find the exact length of the curve.x = t/1 + t, y = ln(1 + t), 0 ≤ t ≤ 2
Sketch the curve with the given polar equation.r2 = cos 4θ
Sketch the curve with the given polar equation.r = 2 cos(3θ/2)
Find the exact length of the polar curve.r = 3 sin θ, 0 ≤ θ ≤ π/3
Sketch the curve with the given polar equation.r = 1 + 2 cos 2θ
Sketch the curve with the given polar equation.r2θ = 1
Graph the curve and find its length.x = et – t, y = 4et/2 –8 ≤ t ≤ 3
Sketch the curve with the given polar equation.r = 1 + 2 cos(θ/2)
Use a calculator to find the length of the curve correct to four decimal places.r = 3 sin 2θ
Use a calculator to find the length of the curve correct to four decimal places.r = 4 sin 3θ
Use a calculator to find the length of the curve correct to four decimal places.r = sin(θ/2)
Test the series for convergence or divergence. 1 Σ n=1 n + 3"
Use a calculator to find the length of the curve correct to four decimal places.r = 1 + cos (θ/3)
Test the series for convergence or divergence. Σ n=1 (2n + 1)" 2n 72
A function f is defined by Where is f continuous? Xx 2n - 1 f(x) = lim 2n 1100 X +1
Graph the curve and find its length.r = cos4 (θ/4)
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. 00 Σ n=0 (-10)" n!
Test the series for convergence or divergence.4/7 – 4/8 + 4/9 – 4/10 + 4/11 – · · ·
Find the Taylor polynomial Tn(x) for the function f at the number a. Graph f and T3 on the same screen.f(x) = 1/x, a = 2
Find the radius of convergence and interval of convergence of the series. Σ n=1 vn
Find the radius of convergence and interval of convergence of the series. 00 (-1)"x" n=0 n + 1
List the first five terms of the sequence.an = 1 – (0.2)n
Test the series for convergence or divergence. 1 2 1 3 1 4 1 √√5 + 1 √√6
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Σ (-1) "12" n=1 72 n
Test the series for convergence or divergence. Σ (−1)" – n=1 n της + 2 n
Find the Taylor polynomial Tn(x) for the function f at the number a. Graph f and T3 on the same screen.f(x) = x + e–x, a = 0
Find the radius of convergence and interval of convergence of the series. Σ M=1 (-1)"-¹x" 3 n³
Test the series for convergence or divergence. 00 Σ Ν M=1 (-1)"-1 2n + 1
List the first five terms of the sequence.an = n +1/3n – 1
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Σ n=1 (-1)"+¹ 4 Η
Test the series for convergence or divergence. 00 m=1 n 22"-1 (-5)"
Find the radius of convergence and interval of convergence of the series. 00 Σvnx" n=1
Test the series for convergence or divergence. n=1 (-1)"-¹ In(n + 4)
List the first five terms of the sequence.an = 3(–1)n/n!
Test the series for convergence or divergence. 00 1 Σ n=1 2n + 1
Test the series for convergence or divergence. D(-1)" n=1 3n - 1 2n + 1
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. 00 Σ (3)* Κ k=1
List the first five terms of the sequence.(2 · 4 · 6 · · · · · · · (2n)}.
Test the series for convergence or divergence. 00 1 Σ n=2 nv In n
Find the Taylor polynomial Tn(x) for the function f at the number a. Graph f and T3 on the same screen.f(x) = arcsin x, a = 0
Find the radius of convergence and interval of convergence of the series. 00 Σ n=1 71.71 ru
Test the series for convergence or divergence. Σ (-1)*. n=1 n 3 In + 2
List the first five terms of the sequence.a1 = 3, an+1 = 2an – 1
Find the radius of convergence and interval of convergence of the series. n²x" Σ (-1)". 2" n=1
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Σ n=1 n! 100"
Determine whether the series is convergent or divergent. 00 Σ n=1 n 2 0.85
Find the Taylor polynomial Tn(x) for the function f at the number a. Graph f and T3 on the same screen.f(x) = ln x/x, a = 1
Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] Also find the associated radius of
List the first five terms of the sequence.a1 = 4, an+1 = an/an – 1
Test the series for convergence or divergence. 00 Σ (-1)" - n=1 P 10"
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. 00 Σ (-1)". )n (1.1)* - nt n=1
Test the series for convergence or divergence. Σke* k=1
Determine whether the series is convergent or divergent. 00 Σ (n-14 + 3n ~12) n=1
Find the radius of convergence and interval of convergence of the series. Σ n=1 10"x" 3 H
Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] Also find the associated radius of
Test the series for convergence or divergence. Υπ 1 + 2√√n Σ (-1)"- n=1
Test the series for convergence or divergence. 00 Enter Σ n=1
Find the radius of convergence and interval of convergence of the series. Σ n=1 (-2)"x" 4, n 1
Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] Also find the associated radius of
Test the series for convergence or divergence. n² n3 + 4 00 Σ (-1)+1, n=1
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Σ n=1 (−1)"el/n 3 n
Determine whether the series is convergent or divergent. 1 + + + 2/2 3/3 4/4 ' 5/5
Test the series for convergence or divergence. 00 (-1)"+1 Σ m=2 n Inn
Find the radius of convergence and interval of convergence of the series. 00 Σ n=1_5*,5 Η X
Test the series for convergence or divergence. 00 1/n Σ (-1)*1 el/% M1=1 n
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Σ n=1 sin 4n 4"
Test the series for convergence or divergence. 00 Σ sin n n=1
Find the radius of convergence and interval of convergence of the series. Σ (−1)". n=2 4" In n
Test the series for convergence or divergence. n Σ (-1)", In m n=2

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