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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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TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT

Transcribed Image Text:Solution:
1-
2-
Tangent line of
= f'(t) = < =// (++)), d (1²+1), d (2²+D)>,
d
dt
dt
dt
च
=
Given.
3
f(t) = <++1 +²+1, ²²³+1>.
f'ctl= d <+1, 2+1, 3+1>
|f²CH) = < 1₁ 2+₁ 3+²>,
=
=
-= 20+1, 0²+1, 0²³+1> ++. <.1, 2x0, 3x0²>
< 1, |, |>. + t. < 1, 0, 07.
< 1₁ 1₁ 1 > + < +₁0, 07
=
:: Tangent line
=
f(0) + +· f'lo).
=
= <l+ +₁ 1₁ 12
of f(t) at f(o).
flol =
flo).
fro).
Given.
2+
flt) = <et +₁₁ e²+ +1₁
+1,
=
1
= <e° +1₂ +1, 2° +1>
eº+1, eº+ış
= < eº + 1₁
< 1+1, (+1,
* | f'(t) = <et, 2e2+ 2+. et
<2, 2,2>
f'(H= =// < e² +1₁ e²+ +1,
et
dt
<++1, 1, 1>.
f'(o)= < e²₁ 20²x0 2x0x e0²>
= < 1, 2 eº,
< 1, 2X1, o>,
= < 1, 2, 07
Now fangent line at flo).
f(0) + f. f'(o).
<2,2₁27++. < 1, 2,07
रशशुश + ati ati 0%
<t+2, 2++2, 2>
et² ti
1+1>
07
>
Any
Ans.
et² +17.
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