Please answer all parts. and include the picture of your solution. Thanks 3a.Let f,g: A CR → R and c € A'. Assume that there is a d > 0 such that ƒ (x) = g(x) forall x € A such that 0 < x − c < 8. Show that if lim f (x) exist then limg(x) exists andX→CNotice that if lim f (x)X-C0 < |x − c| < 8₁, then |ƒ (x) − L| < €.lim f (x) = lim g(x).x→CX-CIn other words, lim f (x) depends only on the values of f (x) for x near c -x-aby saying that limits are a "local property".=x→CL exists then for € > 0, there is 0 < 6₁ ≤ 6, such that, for all x € A, ifArgue that lim g (x) exists andx→Cthis fact is often expressedShow that, for all x ¤ A, if 0 < |x − c| < 8₁, then |g (x) − L| < €.lim f (x) = lim g(x).X-CX→CExplain the meaning of the expression that limits are a "local property".

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3a. Let f,g: ACR → R and c E A'. Assume that there is a 6> 0 such that f (x) = g(x) for all x € A such that 0 < x − c < 6. Show that if lim f (x) exist then limg (x) exists and x-c x-c lim f (x) x-c = limg(x). Argue that lim g(x) exists and x-c x-c In other words, lim f (x) depends only on the values of f (x) for x near c- this fact is often expressed by saying that limits are a "local property". x→a Notice that if lim f (x) = L exists then for € > 0, there is 0 < 6₁ ≤ 6, such that, for all x € A, if 0< x- c < 6₁, then f (x) - L < €. x-c Show that, for all x € A, if 0 < |x − c < 8₁, then [g (x) − L| < €. lim f (x) = limg(x). x-c x-C Explain the meaning of the expression that limits are a "local property".

3a. Let f,g: ACR → R and c E A'. Assume that there is a 6> 0 such that f (x) = g(x) for all x € A such that 0 < x − c < 6. Show that if lim f (x) exist then limg (x) exists and x-c x-c lim f (x) x-c = limg(x). Argue that lim g(x) exists and x-c x-c In other words, lim f (x) depends only on the values of f (x) for x near c- this fact is often expressed by saying that limits are a "local property". x→a Notice that if lim f (x) = L exists then for € > 0, there is 0 < 6₁ ≤ 6, such that, for all x € A, if 0< x- c < 6₁, then f (x) - L < €. x-c Show that, for all x € A, if 0 < |x − c < 8₁, then [g (x) − L| < €. lim f (x) = limg(x). x-c x-C Explain the meaning of the expression that limits are a "local property".

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.1: Limits

Problem 9E

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