Let ginl=√1+an To find: (i) g'(x) cliij Domain of g(x) Domain of gix. Q using definition @ g'xl lim gx+h)-g(x) h-to h By = I'm √₁+2(x+h) -√√1+2x ho h = lim (√₁+2in+h)-√₁+2x) (√²+2(x+8) + √₁+2×) ho h √1+21x+h) + √1+2x) = lim hto = lim h-to h-to lim h-to 1+2(x+h)-(1+2x) h ( √1+2(1+h) + √1+2×) 1+2x+2h-1-2X h (√₁+2(x+h) + √²+2x) 2h h(√√1+2+6) + √1+2x 2 √√1+2+3h + 2 √1+2n + √1+2x √₁+2x = 2 √√₁+2 a g'(x g'(x) Domain of 9 2√1+2x √1+2X 90x0: 1+ax>0 2017-1 기호 Domain g(x) is (900) Domain of g'ox is also (-1/200) of
Let ginl=√1+an To find: (i) g'(x) cliij Domain of g(x) Domain of gix. Q using definition @ g'xl lim gx+h)-g(x) h-to h By = I'm √₁+2(x+h) -√√1+2x ho h = lim (√₁+2in+h)-√₁+2x) (√²+2(x+8) + √₁+2×) ho h √1+21x+h) + √1+2x) = lim hto = lim h-to h-to lim h-to 1+2(x+h)-(1+2x) h ( √1+2(1+h) + √1+2×) 1+2x+2h-1-2X h (√₁+2(x+h) + √²+2x) 2h h(√√1+2+6) + √1+2x 2 √√1+2+3h + 2 √1+2n + √1+2x √₁+2x = 2 √√₁+2 a g'(x g'(x) Domain of 9 2√1+2x √1+2X 90x0: 1+ax>0 2017-1 기호 Domain g(x) is (900) Domain of g'ox is also (-1/200) of
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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Transcribed Image Text:CV
Let girl = √√1+28
To find:
(1) g'(x)
ciij
iii)
Domain of gin)
Domain of girl.
By using
9x1= lim gix+h)-glu)
ho
h
= lim
ho
= 1m √√1+2(x+h) -√√1+2x
hto
= lim
=
-
= lim
hto
definition :
(1
=
hto
lim
hto
lim
ho
h
√₁+2(x+h1-√₁+2x) (√₁+2in+B) + √[1+2x)
h
(√₁+2(x+h) + √1+24)
1+2(x+h)-(1+3x)
h ( √1+2(n+h) + √₁+24)
1+2n+2h-1-21
h (√1+2(x+h1+√√√+2×)
2h
h (√√√1+2+h) + √1+2×
2
1+2n+2h + √√√₁+2n
=
√+an+ah
2
1+2n + √√1+24
2
2 √₁+ 2n
to
3
+ g'(x)
-
→g'(x)
=
Domain of
2
2√√√√+2K
1+2X
нях
g(x:
1+2x>0
120-1
기
17-1/22
Domain of girl is
27-1
(-1900)
Domain of glow is also (-1/200)
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