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4. Let f and g be functions defined on an open interval I containing the point z = a. Suppose that lim f(x) = -3, lim h(x) = 7, and lim g(x) = 0. Evaluate the limit if it exists. Enter your simplified 2-a x→a x→a Show all work in the answer in the square bracketed space. If the limit does not exist, write DNE. space provided. (a) (b) (c) lim (2h(x) - 3f (x)) = x-a 2f(x) z-a /f(x)² +h(x) lim f(x) lim z-a g(x) ||

4. Let f and g be functions defined on an open interval I containing the point z = a. Suppose that lim f(x) = -3, lim h(x) = 7, and lim g(x) = 0. Evaluate the limit if it exists. Enter your simplified 2-a x→a x→a Show all work in the answer in the square bracketed space. If the limit does not exist, write DNE. space provided. (a) (b) (c) lim (2h(x) - 3f (x)) = x-a 2f(x) z-a /f(x)² +h(x) lim f(x) lim z-a g(x) ||

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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4. Let f and g be functions defined on an open interval I containing the point z = a. Suppose that lim f(x) = -3, lim h(r) = 7, and lim g(x) = 0. Evaluate the limit if it exists. Enter your simplified answer in the square bracketed space. If the limit does not exist, write DNE. Show all work in the space provided. x-a I-a (a) (b) (c) D-I Hint: Suppose that lim lim (2h(r)-3f(x)) = x→a lim x→a z-a 9(2) 2f(x) √f(x)² +h(x) lim I-a f(x) g(x) = L exists. Observe that f(x) = = f(x) 9(x) *9(x).
Transcribed Image Text:4. Let f and g be functions defined on an open interval I containing the point z = a. Suppose that lim f(x) = -3, lim h(r) = 7, and lim g(x) = 0. Evaluate the limit if it exists. Enter your simplified answer in the square bracketed space. If the limit does not exist, write DNE. Show all work in the space provided. x-a I-a (a) (b) (c) D-I Hint: Suppose that lim lim (2h(r)-3f(x)) = x→a lim x→a z-a 9(2) 2f(x) √f(x)² +h(x) lim I-a f(x) g(x) = L exists. Observe that f(x) = = f(x) 9(x) *9(x).
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