Given that, we need to find the derivative of texs and domain of function and its derivative. Note: Domain of function! points of S. Here, i-e.. Hence, where Now f're) = lim freth) - f(a) hyo h => f'ox) = fex: fee) is a rational function, and it is not defined when its denominator is zero. 1-3x =0 => x= 3. Domain of fev = 3+x 1-3x Ris set of real number. fer is fox) = 3+x 1-3x A set S is called domain of fex) if fex) is defined for all = lim ho derivative of li'm I nyo n to lim t n 3+x 1-3x 13+x+h 1-3X-3h 1 (use this definition) 3+x 1-3x R-{£3. h (3+x+h) (1-3x)- (3+x)(1-3X-3h) 13x-32)] (1-3x-3h) (1-3X) -9x+x-3x²+h-3xh-3+4x²+xh-x+3x²473xh] (1-3X-3h) (1-3X)
Given that, we need to find the derivative of texs and domain of function and its derivative. Note: Domain of function! points of S. Here, i-e.. Hence, where Now f're) = lim freth) - f(a) hyo h => f'ox) = fex: fee) is a rational function, and it is not defined when its denominator is zero. 1-3x =0 => x= 3. Domain of fev = 3+x 1-3x Ris set of real number. fer is fox) = 3+x 1-3x A set S is called domain of fex) if fex) is defined for all = lim ho derivative of li'm I nyo n to lim t n 3+x 1-3x 13+x+h 1-3X-3h 1 (use this definition) 3+x 1-3x R-{£3. h (3+x+h) (1-3x)- (3+x)(1-3X-3h) 13x-32)] (1-3x-3h) (1-3X) -9x+x-3x²+h-3xh-3+4x²+xh-x+3x²473xh] (1-3X-3h) (1-3X)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Given that,
we need to find the derivative of tex and
domain of function and its derivative.
Note;
Domain of function!
points of S.
Here,
i-e..
Hence,
where
Now
f're) = lim freth) - f(a)
hyo
h
=> f'ox) =
fex:
fee is
a
rational function, and it is not
defined when its denominator is zero.
1-3x =0
=> x = 3
Domain of fev = 3+x
1-3x
Ris
set of real numbers.
fer is
A set S is called domain of
fex) if fox) is defined for all
=
lim
ho
derivative of
fox) = 3+x
1-3x
to lim
lim I
nyo
n
3+x
1-3x
13+x+h
1-32-3h
n
1
(use this definition)
3+x
1-3x
R-{£3.
h
(3+x+h) (1-3x) (3+x)(1-3X-3h)
-3x-3h)]
(1-3X-3h) (1-3X)
-9x+x-3x²4th-3xh-3+4x²+xh-x+3x²+3xh]
(1-3X-3h) (1-3X)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2bd53856-3781-4921-9803-0fa9b48c3930%2F330e2fbb-c5a7-40b9-8883-a4c4d8cbbe21%2Fqrpm7qn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given that,
we need to find the derivative of tex and
domain of function and its derivative.
Note;
Domain of function!
points of S.
Here,
i-e..
Hence,
where
Now
f're) = lim freth) - f(a)
hyo
h
=> f'ox) =
fex:
fee is
a
rational function, and it is not
defined when its denominator is zero.
1-3x =0
=> x = 3
Domain of fev = 3+x
1-3x
Ris
set of real numbers.
fer is
A set S is called domain of
fex) if fox) is defined for all
=
lim
ho
derivative of
fox) = 3+x
1-3x
to lim
lim I
nyo
n
3+x
1-3x
13+x+h
1-32-3h
n
1
(use this definition)
3+x
1-3x
R-{£3.
h
(3+x+h) (1-3x) (3+x)(1-3X-3h)
-3x-3h)]
(1-3X-3h) (1-3X)
-9x+x-3x²4th-3xh-3+4x²+xh-x+3x²+3xh]
(1-3X-3h) (1-3X)
![f'(x) = lim —
= [(1-3X
n
ho
=) t'oxo =
=)
ΟΥ
50]
(1-3x-3h) (1-3x))
applying the limits
f100 =
Now,
lim
ho
and
10h
+'(x) =
10
(1-3X-3h) (1-3x)
16
(1-3x) (1-3X)
flox) is also a rational function.
(1-3x)² = 0 <=> x = }}
therefore, Domain of flees is also R-{3}.
(1-3x)2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2bd53856-3781-4921-9803-0fa9b48c3930%2F330e2fbb-c5a7-40b9-8883-a4c4d8cbbe21%2F326tojc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:f'(x) = lim —
= [(1-3X
n
ho
=) t'oxo =
=)
ΟΥ
50]
(1-3x-3h) (1-3x))
applying the limits
f100 =
Now,
lim
ho
and
10h
+'(x) =
10
(1-3X-3h) (1-3x)
16
(1-3x) (1-3X)
flox) is also a rational function.
(1-3x)² = 0 <=> x = }}
therefore, Domain of flees is also R-{3}.
(1-3x)2
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