Proof Prove that if the limit of f ( x ) as x approaches c exists, then the limit must be unique. [ Hint : Let lim x → c f ( x ) = L 1 and lim x → c f ( x ) = L 2 and prove that L 1 = L 2 . ]
Proof Prove that if the limit of f ( x ) as x approaches c exists, then the limit must be unique. [ Hint : Let lim x → c f ( x ) = L 1 and lim x → c f ( x ) = L 2 and prove that L 1 = L 2 . ]
Solution Summary: The author explains that if f(x) as x approaches c exists, then the limit must be unique.
Proof Prove that if the limit of f (x) as x approaches c exists, then the limit must be unique. [Hint: Let
lim
x
→
c
f
(
x
)
=
L
1
and
lim
x
→
c
f
(
x
)
=
L
2
and prove that
L
1
=
L
2
.
]
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]
DETAILS
MY NOTES
SESSCALCET2 6.3.508.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.)
x + 16
dx
X
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13. [-/1 Points]
DETAILS
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]
DETAILS
MY NOTES
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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DETAILS
MY NOTES
SESSCALCET2 6.3.012.
6. [-/1 Points]
Evaluate the integral.
x-4
dx
x²
- 5x + 6
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7. [-/1 Points]
DETAILS
MY NOTES
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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8. [-/1 Points] DETAILS
MY NOTES
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
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