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1 Use the graph and algebra to approximate the largest value of 8 or smallest-magnitude N that corresp to the given value of or M, according to the appropriate formal limit definition. a) lim √x-1=2, ε = 1 15 b) lim d) lim(4-x²)=-∞, M = 10000 1 -∞, M = 100 c) lim -=1, &=0.5 81 x+1

1 Use the graph and algebra to approximate the largest value of 8 or smallest-magnitude N that corresp to the given value of or M, according to the appropriate formal limit definition. a) lim √x-1=2, ε = 1 15 b) lim d) lim(4-x²)=-∞, M = 10000 1 -∞, M = 100 c) lim -=1, &=0.5 81 x+1

Advanced Engineering Mathematics
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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O.If th ment-4-c64d9 sect G LZ 11x a) lim √x-1=2, e = 1 x-5 pro Use the graph and algebra to approximate the largest value of 8 or smallest-magnitude N that corresponc to the given value of or M, according to the appropriate formal limit definition. d) lim(4-x²)=-∞, M = 10000 CSC N. Nun N. SOL (X CCh P MAT G gra 1 b) lim xl'x²-1 =-∞, M = 100 c) lim=1, -0.5 *x+1 Ans + Drag and drop an image or PDF file or click to browse...
Transcribed Image Text:O.If th ment-4-c64d9 sect G LZ 11x a) lim √x-1=2, e = 1 x-5 pro Use the graph and algebra to approximate the largest value of 8 or smallest-magnitude N that corresponc to the given value of or M, according to the appropriate formal limit definition. d) lim(4-x²)=-∞, M = 10000 CSC N. Nun N. SOL (X CCh P MAT G gra 1 b) lim xl'x²-1 =-∞, M = 100 c) lim=1, -0.5 *x+1 Ans + Drag and drop an image or PDF file or click to browse...
Expert Solution
Step 1

a) limx→5x-1=2 , ε=1

Use definition of limit

x-1-2<ε⇔2-ε<x-1<2+ε⇔2-1<x-1<2+1⇔1<x-1<3

1<x-1⇔1<x-1⇔1+1<x⇔2<x

x-1<3⇔x-1<9⇔x<10

Taking N=10 , we have

x∈2,10⇒x-1-2<∈

So, the largest N is 10

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