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mathematics
calculus early transcendentals 9th

Questions and Answers of Calculus Early Transcendentals 9th

Evaluate the integral. π/3 sec 0 tan 0 de
Evaluate the definite integral. X J1 2 2 X dx
Evaluate the indefinite integral. /cot x csc²x dx
Evaluate the integral by interpreting it in terms of areas. (5 (10 - 5x) dx -2
Evaluate the integral, if it exists. X E-x x - 3 хр-
Evaluate the integral. √ √² + sint dt
Evaluate the definite integral. √y-y dy .y y2
Evaluate the indefinite integral. COS(π/x) .2 dx
Evaluate the integral, if it exists. f x(1 - x)²/³ dx
Evaluate the integral. 1² ( 2x + 1) dx
Evaluate the integral, if it exists. */*(1 + tan 1)³ sec²t dt Jo
Evaluate the definite integral. fx (√x + √x) dx
Evaluate the indefinite integral. cos (1 + 5t) dt
Evaluate the integral. ²₁ (3u − 2)(u + 1) du -1
Evaluate the definite integral. *#/2 ¹/2 (√t - 3 cos t) dt Jo
(a) Use the form of the definition of the integral to evaluate the given integral.(b) Confirm your answer to part (a) graphically by interpreting the integral in terms of areas. -1 (2 − 1x) dx -
Evaluate the indefinite integral. sin cos 1 + sin²0 - do
Evaluate the integral, if it exists. sec 0 tan 0 1 + sec 0 - do
Evaluate the integral. t. 2+x² x -dx
Evaluate the indefinite integral. 5' sin(5¹) dt
Evaluate the definite integral. π/3 Jw/6 (4 sec²y) dy
(a) Use the form of the definition of the integral to evaluate the given integral.(b) Confirm your answer to part (a) graphically by interpreting the integral in terms of areas. 3 So 4x dx
Evaluate the integral. (4-1) √t dt
Evaluate the indefinite integral. S 1 (rẻ + 1)arctan x dx
Evaluate the definite integral. 4 Jo 1 + p² dp
Evaluate the integral, if it exists.∫ sinh(1 + 4x) dx
Evaluate the integral, if it exists. 3 X 1 + x4 dx
Evaluate the integral. Jo (u + 2)(u - 3) du
Evaluate the definite integral. St ( 4 + 6u √u du
Evaluate the integral. 5 Se dx -5
Evaluate the indefinite integral. (arctan x)2 x² + 1 -dx
Evaluate the definite integral. ƒ¹, 1(1 − 1)² dt. J-1
Use the form of the definition of the integral to evaluate the integral. f² (2x - x³) dx
Evaluate the indefinite integral. sec²x tan²x -dx
Evaluate the integral. cos e de
Evaluate the integral, if it exists. f tan x In(cos x) dx
Evaluate the definite integral. S²³ 3x² + 4x + 1 dx
Evaluate the indefinite integral. sec²0 tan 0 - dᎾ
Use the form of the definition of the integral to evaluate the integral. f (x² – 3x²) dx
Evaluate the integral, if it exists. sin (In x) -dx X
Evaluate the definite integral. 4 (2 K² (+ / - 13 ) dx X
Evaluate the integral. ²² ( ² + ² ) J zp
Evaluate the indefinite integral. arcsin x /1-x² -dx
Use the form of the definition of the integral to evaluate the integral. √²₁ (4x² + x + 2) dx J-1
Evaluate the integral, if it exists. eva X -dx
Evaluate the integral. S* (1² + 13/2) dt
Evaluate the indefinite integral. fer(2 + 3er) ³/² dr
Evaluate the definite integral. ²(2x - 3)(4x² + 1) dx
Use the form of the definition of the integral to evaluate the integral. √₁² (3x² + 7x) dx
Evaluate the integral. 8. S³x-2/³ dx
Evaluate the integral, if it exists.∫ sin x cos(cos x) dx
(a) Use the Direct Comparison Test to show that the first series diverges by comparing it to the second series.(b) Use the Limit Comparison Test to show that that the first series diverges by
Two similar-looking series are given. Test each one for convergence or divergence.a.b. น I + u [-u M 8
List the first five terms of the sequence. an 1 3" + 1
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 Σcn6n is convergent, then Σcn(–2)n is
Find the radius of convergence and interval of convergence of the power series. 00 Σ (-1)^nx" n=1
Determine whether the sequence is convergent or divergent. If it is convergent, find its limit.an = cos(nπ/2)
Test the series for convergence or divergence. 1 In 3 1 In 4 + 1 In 5 1 In 6 + 1 In 7
Use the Integral Test to determine whether the series is convergent or divergent. Ση d=1 -0.3
Use the Ratio Test to determine whether the series is convergent or divergent. 00 (-2)" n²
Which of the following inequalities can be used to show thatconverges?a.b.c. Σ=n/(n + 1)
Two similar-looking series are given. Test each one for convergence or divergence.a.b. Σ n- m=1 n 2 n? + 1
List the first five terms of the sequence. {2" + + n}" =2
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 Σcn6n is convergent, then Σcn(–6)n is
Find the radius of convergence and interval of convergence of the power series. 50 Στηx" n=1
Determine whether the sequence is convergent or divergent. If it is convergent, find its limit. an n sin n n² + 1
Test the series for convergence or divergence. Τ WE Σ (-1)^-1 3 + 5η
Use the Integral Test to determine whether the series is convergent or divergent. 00 Σ n=1 2 5η – 1
Find the radius of convergence and interval of convergence of the power series. Σ =1 (-1)"x" ψη
Determine whether the sequence is convergent or divergent. If it is convergent, find its limit. an In n 'n
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 Σcnxn diverges when x = 6, then it
List the first five terms of the sequence. 2 ก n² + 1 DG n=3
Two similar-looking series are given. Test each one for convergence or divergence.a.b. 8 In n n-1 n
Which of the following inequalities can be used to show thatdiverges?a.b.c. Σ=ın/(n? + 1)
Use the Ratio Test to determine whether the series is convergent or divergent. Σ (−1)"-1 x=1 3" 2" m 3
Find a power series representation for the function and determine the interval of convergence. f(x) = 1 1-x²
Use the Integral Test to determine whether the series is convergent or divergent. 1 Σ 4 n=1 (3η – 1)+
Use the Ratio Test to determine whether the series is convergent or divergent. Σ n=0 (-3)" (2n + 1)!
(a) If a series is convergent by the Integral Test, how do you estimate its sum?(b) If a series is convergent by the Direct Comparison Test, how do you estimate its sum?(c) If a series is convergent
Find a power series representation for the function and determine the interval of convergence. f(x) = x + a x² + a²¹ a>0
Two similar-looking series are given. Test each one for convergence or divergence.a.b. 8 1 Σ n=\ n + n!
List the first five terms of the sequence. an (-1)^-1 2
Find the radius of convergence and interval of convergence of the power series. n 5" "X"
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.The Ratio Test can be used to determine
Test the series for convergence or divergence. D(-1)" x=1 3n - 1 2n + 1
Determine whether the sequence is convergent or divergent. If it is convergent, find its limit.{(1 + 3/n)4n}
Use the Integral Test to determine whether the series is convergent or divergent. nt Σ n=2 n’ + 1 3
Calculate the first eight terms of the sequence of partial sums correct to four decimal places. Does it appear that the series is convergent or divergent? 00 Σ(-1)" n n=
Use the Ratio Test to determine whether the series is convergent or divergent. 00 k=1 -1 k!
Two similar-looking series are given. Test each one for convergence or divergence.a.b. 00 Σ n=l 1 /n2 + 1 +1
List the first five terms of the sequence. an (-1)" 4"
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.The Ratio Test can be used to determine
Find the radius of convergence and interval of convergence of the power series. 00 5″ -x" n=2 n
Determine whether the sequence is convergent or divergent. If it is convergent, find its limit.{(–10)n/n!}
Test the series for convergence or divergence. της n? + n + 1 Σ (-1)" - n=1
Use the Integral Test to determine whether the series is convergent or divergent. 8 Ente-n3 n=1
Use the Ratio Test to determine whether the series is convergent or divergent. Σke* k=1
Use the Ratio Test to determine whether the series is convergent or divergent. Σ n=1 10" (n + 1) 42n+1
Determine whether the series converges or diverges. n + 1 Σ n=1 Ma n√n
Suppose f(x) is the sum of a power series with radius of convergence R.(a) How do you differentiate f ? What is the radius of convergence of the series for f'?(b) How do you integrate f ? What is the

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