(x−7)(x−3)* Give a step-by-step e-6 proof that lim Q(x) = Q(2). #-2
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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can you please write this part in handwriting? the characters are in different format so im having a hard time understanding
Given function: Q(x)=52x+1x-7x-3
To show: limx→2Q(x)=Q(2) byε-δ method.
Definition: ∀ε ∃δ |x-a|<δ ⇒ |f(x)-f(a)|<ε
Q(x)=52x+1x-7x-3
Now, Q(2)=55-5-1=5
Then Q(x)-Q(2)=52x+1x-7x-3-5=-5x-7x-3+52x+1x-7x-3=-5x2+60x-100x-7x-3
Choose δ≤ε where -5x2+60x-100x-7x-3<δ
Therefore Q(x)-Q(2)=-5x2+60x-100x-7x-3<ε
Thus, Q(x)-Q(2)<ε whenever -5x2+60x-100x-7x-3<δ
Q(x) is continuous at x=2
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