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mathematics
calculus 6th edition

Questions and Answers of Calculus 6th edition

Find the limit, if it exists, or show that the limit does not exist. lim (x, y, z)→ (3, 0, 1) e -xy sin(72/2)
Find the limit, if it exists, or show that the limit does not exist. lim (x, y, z) → (0,0,0) x² + 2y² + 3z² 2 x² + y² + z²
Find the limit, if it exists, or show that the limit does not exist. yz lim 2 (x,y,z) (0.0.0) x² + 4y² + 9z²
Graph the function and observe where it is discontinuous. Then use the formula to explain what you have observed.f(x, y) = e1/(x – y)
Let f(x, y) = x2e3xy. (a) Evaluate f(2,0). (b) Find the domain of f.(c) Find the range of f.
Find and sketch the domain of the functionWhat is the range of f? f(x, y) = √1 + x − y².
Let (a) Evaluate f(2, –1, 6). (b) Find the domain of f.(c) Find the range of f. f(x, y, z) = √²-x²-y² 2-
Let g(x, y, z) = ln(25 – x2 – y2 – z2). (a) Evaluate g(2, –2, 4). (b) Find the domain of g.(c) Find the range of g.
Find and sketch the domain of the function.f(x, y) = √x + y
Find and sketch the domain of the function.f(x, y) = √xy
Find and sketch the domain of the function.f(x, y) = √y – x ln(y + x) -
Find and sketch the domain of the function.f(x, y) = √1 – x2/√1 – y2
Find and sketch the domain of the function.f(x, y) = √y + √25 – x2 – y2
Find and sketch the domain of the function.f(x, y) = arcsin(x2 + y2 – 2)
Find and sketch the domain of the function.kf(x, y, z) = √1 – x2 – y2 – z2
Sketch the graph of the function.f(x, y) = 3
Sketch the graph of the function.f(x, y) = y
Sketch the graph of the function.f(x, y) = cos x
Sketch the graph of the function.f(x, y) = y2 + 1
Sketch the graph of the function.f(x, y) = 3 – x2 – y2
Sketch the graph of the function.f(x,y) = √16x – x2 – 16y2
Sketch the graph of the function.f(x, y) = √x2 + y2
Draw a contour map of the function showing several level curves. f(x, y) = (y – 2x)2
Draw a contour map of the function showing several level curves.f(x, y) = x3 – y
Draw a contour map of the function showing several level curves.f(x, y) = y – ln x
Draw a contour map of the function showing several level curves.f(x, y) = ey/x
Draw a contour map of the function showing several level curves.f(x, y) = y sec x
Draw a contour map of the function showing several level curves.f(x, y) = √y2 – x2
Use a computer to graph the function using various domains and viewpoints. Get a printout of one that, in your opinion, gives a good view. If your software also produces level curves, then plot some
Describe how the graph of g is obtained from the graph of f. (a) g(x, y) = f(x, y) + 2 (c) g(x, y) = -f(x, y) (b) g(x, y) = 2f(x, y) (d) g(x, y) = 2 -f(x, y)
Use a computer to graph the function using various domains and viewpoints. Get a printout of one that, in your opinion, gives a good view. If your software also produces level curves, then plot some
Describe the level surfaces of the function.f(x, y, z) = x2 – y2
Find the limit. lim (cost, sint, t ln t) 1-0+
Reduce the equation to one of the standard forms, classify the surface, and sketch it.4y2 + z2 – x – 16y – 4z + 20 – 0
Find the length of the curve.r(t) = 〈2 sin t, 5t, 2 cos t〉, –10 ≤ t ≤ 10
Test the series for convergence or divergence. 00 Σ n=1 (-2)2 n'
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Σ n=1 n' + 1 +1 2n² + 1/ Π
Test the series for convergence or divergence. 00 Σ (−1)" 21/n n=1
Determine whether the series is convergent or divergent. Σ 2 n=1 n 1 – 4n + 5 ·
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. 00 n=1 (-2)" n"
Determine whether the series is convergent or divergent. 1 Σ n=2 n In n
Determine whether the series is convergent or divergent. n I - u^ - I + u/ n=1 Σ
Find the radius of convergence and interval of convergence of the series. 00 Σ n=1 n(x – 4)" n3 + 1
Determine whether the series is convergent or divergent. 00 Σ n=2 1 n(ln n)2
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Σ n=2 -2n (n+1) 5n
Test the series for convergence or divergence. 00 vnt - 1 Σ n=1 n3 + 2n’ + 5
Find the radius of convergence and interval of convergence of the series. Σ n!(2x − 1)" n=1
Determine whether the series is convergent or divergent. ellin Σ n=1 n n’
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Σ n=1 1 + 71 2
Test the series for convergence or divergence. Σ tan(1/n) n=1
Find the radius of convergence and interval of convergence of the series. Σ M=1 21 HX ²x" 2.4.6. . (2n)
Determine whether the series is convergent or divergent. Σ n=3 n e 71
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Σ M=1 72 (11 n)"
Prove that if n > 1, the partial sum of the harmonic series is not an integer.Let 2K be the largest power of 2 that is less than or equal to n and let M be the product of all odd integers that are
Test the series for convergence or divergence. Σn sin(1/n) n=1
Find the radius of convergence and interval of convergence of the series. Σ n=1 (4x + 1)" ne 2
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. 1 1.3 3! 1.3.5 5! + (−1)n-1¹ · 3 · 5. + 1.3.5.7 7! . (2n-1) (2n - 1)! + +.
Determine whether the series is convergent or divergent. 00 1 Σ 3 n=1 n’ + n ζ
Test the series for convergence or divergence. n! Σ Μ' h=1€
Find the radius of convergence and interval of convergence of the series. 00 Σ n=2 71 X n(1n n)2
Use the binomial series to expand the function as a power series. State the radius of convergence.k√1 + x
Determine whether the series is convergent or divergent. 00 n Σ n=int + 1 M=1
Test the series for convergence or divergence. 00 n=1 n² + 1 5"
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. 2 5 + 2.6 5.8 + 2.6.10 5.8.11 + 2.6 10 14 5 8 11 14
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Σ n=1 2.4.6. n! • (2n)
Use the binomial series to expand the function as a power series. State the radius of convergence.1/(1 + x)4
Determine whether the sequence converges or diverges. If it converges, find the limit.an = cos(n/2)
Find the radius of convergence and interval of convergence of the series. Σ n!x" 11.3.5.. (2n-1)
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. 00 Σ (-1)". H1 2*n! 5·8· 11. ... . (3n + 2)
Determine whether the sequence converges or diverges. If it converges, find the limit.an = cos(2/n)
Ifis convergent, does it follow that the following series are convergent?(a)(b) 100 Στο Ch4"
Test the series for convergence or divergence. Σ 1/n 2
Test the series for convergence or divergence. (-1)" n=1 cosh n
Use the binomial series to expand the function as a power series. State the radius of convergence.(1 – x)2/3
Suppose you know thatand the Taylor series of f centered at 4 converges to f(x) for all x in the interval of convergence. Show that the fifth- degree Taylor polynomial approximates f(5) with error
Test the series for convergence or divergence. √j j+5 00 Σ (-1). Fl
Determine whether the sequence converges or diverges. If it converges, find the limit.{arctan 2n}
Test the series for convergence or divergence. (n!)" Σ n=1 n
Test the series for convergence or divergence. Σ n=1 sin(1/n) WH n
Determine whether the sequence converges or diverges. If it converges, find the limit.{n2e–n}
Test the series for convergence or divergence. Σ n=2 1 (1n n )In n
Determine whether the sequence converges or diverges. If it converges, find the limit.{n cos nπ}
Express the number as a ratio of integers. 0.73 0.73737373...
Express the number as a ratio of integers.0.2̅ = 0.2222 · · ·
Express the number as a ratio of integers. 3.417 3.417417417
Find the radius of convergence of the series Σ H=1 (2n)! (n!)² th
Express the number as a ratio of integers. 6.254 = 6.2545454 ...
Express the number as a ratio of integers. 1.5342
Express the number as a ratio of integers. 7.12345
Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?an = (–2)n+1
Find the sum of the series. 00 4n X n! Σ(-1)". n-0
Find the sum of the series. Σ 7-0 2n (−1)" πλη 62 (2n)!
Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?an = 2n – 3/3n + 4
Find the sum of the series. Γ Σ η 0 (-1)" ²n+1 42n+¹(2n + 1)!
Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?an = ne–n
Find the sum of the series. 9 3 + + 2! 27 81 + 3! 4!
Find the sum of the series. 3" Σ no 5*n!
Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?an = n/n2 + 1
Find the sum of the series. 1 - In 2 + (In 2)² 2! (In 2)³ 3! +
Which of the following expressions are meaningful? Which are meaningless? Explain. (a) (a. b). c (c) a (b c) (e) a b + c (b) (a - b)c (d) a . (b + c) (f) a (b + c) .

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