State the Fundamental Theorem of Calculus (Part I and Part II). Hence or otherwise: (a) If u is a differentiable function of a over I, obtain a formula for d (Hint: You may use (c) By Using L'hopital's rule, Hence find (√1+ u^du) dt] . dz² (b) Evaluate i. Evaluate the limit lim 7-0 dz T lim #-3 I I fint dt = F(x) - F(3) for some antidervative F of sint) f(t). sin (22) + 7z² - 2z 2² (2+1)² sin t
State the Fundamental Theorem of Calculus (Part I and Part II). Hence or otherwise: (a) If u is a differentiable function of a over I, obtain a formula for d (Hint: You may use (c) By Using L'hopital's rule, Hence find (√1+ u^du) dt] . dz² (b) Evaluate i. Evaluate the limit lim 7-0 dz T lim #-3 I I fint dt = F(x) - F(3) for some antidervative F of sint) f(t). sin (22) + 7z² - 2z 2² (2+1)² sin t
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:1. State the Fundamental Theorem of Calculus (Part I and Part II). Hence or otherwise:
(a) If u is a differentiable function of a over I, obtain a formula for
Hence find
(b) Evaluate
d²
dz²
[/² (™ √/₁+ u^²du)
lim
#-3
i. Evaluate the limit lim
-0
af f(t).
dz
I
-35² sint dt)
x-3
(Hint: You may use f3 sint dt = F(x) - F(3) for some antidervative F of it)
(c) By Using L'hopital's rule,
sin(22) + 7z² - 2z
2² (2+1)²
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