Useful factorization formula Calculate the following limits using the factorization formula x n − a n = ( x − a ) ( x n − 1 + x n − 2 a + x n − 3 a 2 + ⋯ + x a n − 2 + a n − 1 ) , where n is a positive integer and a is a real number . 73. lim x → a x 5 − a 5 x − a
Useful factorization formula Calculate the following limits using the factorization formula x n − a n = ( x − a ) ( x n − 1 + x n − 2 a + x n − 3 a 2 + ⋯ + x a n − 2 + a n − 1 ) , where n is a positive integer and a is a real number . 73. lim x → a x 5 − a 5 x − a
Solution Summary: The author evaluates the value of undersetxto amathrmlim
Do the Laplace Transformation and give the answer in Partial Fractions. Also do the Inverted Laplace Transformation and explain step-by-step.
12. [-/1 Points]
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SESSCALCET2 6.3.508.XP.
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Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
x + 16
dx
X
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13. [-/1 Points]
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MY NOTES
SESSCALCET2 6.3.512.XP.
ASK YOUR TEA
Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
dx
8)(2x + 1)
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14. [-/1 Points]
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SESSCALCET2 6.3.518.XP.
Find the area of the region under the given curve from 1 to 5.
y =
x² +7
6x - x²
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SESSCALCET2 6.3.012.
6. [-/1 Points]
Evaluate the integral.
x-4
dx
x²
- 5x + 6
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7. [-/1 Points]
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SESSCALCET2 6.3.019.
Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
x²+1
(x-6)(x-5)²
dx
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SESSCALCET2 6.3.021.
Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
✓
x²
4
+4
dx
Chapter 2 Solutions
Student Solutions Manual, Single Variable for Calculus: Early Transcendentals
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