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+h)4-44Q 9 Compute limh-0h

Question
+h)4-44
Q 9 Compute limh-0
h
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+h)4-44 Q 9 Compute limh-0 h

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Step 1

To find:

(h+4)-4
lim
h
h-0
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(h+4)-4 lim h h-0

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Step 2

Solution...

h+4) -4 0(indeterminate form) when h= 0
lim
h0
=
h
Apply L' Hôpital's rule, differentiate both numerator and denominator with respect to h.
4 (h+4) lim4(h+4)
(h+4)-4
lim
h0
lim
h
h0
1
h0
Now when h is 0, there is no more indeterminate form
(h+4)-4
4
- 4 (0+4) 4256
Hence, the limit becomes lim
h0
h
help_outline

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h+4) -4 0(indeterminate form) when h= 0 lim h0 = h Apply L' Hôpital's rule, differentiate both numerator and denominator with respect to h. 4 (h+4) lim4(h+4) (h+4)-4 lim h0 lim h h0 1 h0 Now when h is 0, there is no more indeterminate form (h+4)-4 4 - 4 (0+4) 4256 Hence, the limit becomes lim h0 h

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Tagged in

Math

Calculus

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