Question
Asked Sep 10, 2019

I need help on one more limits question on page 103 of the James Stewart Calculus Eighth Edition textbook: question #31. I am having trouble mostly on the numerator part of the equation and getting my factoring right

(((x+h)^3)-x^3)

hat
e get
20. lim
1
x+2
19, lim
2 x+8
Au +1-3
9+h-3
22. lim
21. lim
-2
h
1
1
(3+h) 3
3
24. lim
23. lim
+t
25, Im -
26. lim
0
0
- 4x+4
4-x
re
28. lim
I2x .x 4
27. lim
16 16
- H)
x2+9 5
29. lim
30. lim
x t 4
(x+ h-x
(x + h
31. lim
32. lim
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hat e get 20. lim 1 x+2 19, lim 2 x+8 Au +1-3 9+h-3 22. lim 21. lim -2 h 1 1 (3+h) 3 3 24. lim 23. lim +t 25, Im - 26. lim 0 0 - 4x+4 4-x re 28. lim I2x .x 4 27. lim 16 16 - H) x2+9 5 29. lim 30. lim x t 4 (x+ h-x (x + h 31. lim 32. lim

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check_circleExpert Solution
Step 1

Given,

 

(x+h-x
lim
h
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(x+h-x lim h

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Step 2

On simplification, we g...

(x+h)-x
lim
0
h
x323h h -x
=lim
(aba3a'b+3ab +b*
h
h0
3xh 3xhh
lim
h(3x2 3xhh
= lim
h
0
lim (3x2 3xh+h*)
= 3.x2
(by applying the limit)
help_outline

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(x+h)-x lim 0 h x323h h -x =lim (aba3a'b+3ab +b* h h0 3xh 3xhh lim h(3x2 3xhh = lim h 0 lim (3x2 3xh+h*) = 3.x2 (by applying the limit)

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