Let Q(x) = 4+2). Give a step-by-step - proof that _lim Q(x) = -1. Start by stating the appropriate definition with the given values substituted (this is the definition for a rational function having real limit at a point, i.e. the e-6 definition). Definition.
Let Q(x) = 4+2). Give a step-by-step - proof that _lim Q(x) = -1. Start by stating the appropriate definition with the given values substituted (this is the definition for a rational function having real limit at a point, i.e. the e-6 definition). Definition.
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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Wksp 5 Q2
PLEASE PLEASE include labeled definition(AS IT APPLIES TO THE QUESTION), scratchwork, graph/sign-chart and proof

Transcribed Image Text:. Let Q(x) = 4(+2). Give a step-by-step - proof that
lim Q(x) = -1.
24-2
Start by stating the appropriate definition with the given values substituted (this is
the definition for a rational function having real limit at a point, i.e. the - definition).
Definition.
Next, sketch the graph or use a sign chart to understand the behaviour near-2. Use
this knowledge to do the scratch work to determine & based on e. (Hint: factoring the
denominator simplifies the expression Q(x) − (−1)| to. The numerator can be
controlled by 6, while the denominator must be controlled by introducing a temporary
bound).
Scratch work.
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would you please write this part in handwriting? because im not sure i understand.
Let Qx=4x+2x2-4=4x-2
Then Q-2=4-2-2=-1
Now, Qx-Q-2=4x-2+1=x+2x-2
Choose δ≤ε where x+2x-2<δ
Qx-Q-2=x+2x-2<ε
Therefore Qx-Q-2<ε whenever x+2x-2<δ
Therefore, Q(x) is continuous at x=-2
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