37-50. Horizontal asymptotes Determine lim f(x) and lim f(x) for the following functions. Then give the horizontalx →∞→ ∞asymptotes of f (if any).44. f(x) ==6x² +14x4 + 3x + 1 86-87. Sketching graphs Sketch a possible graph of a function f that satisfies all of the given conditions. Be sure to identifyall vertical and horizontal asymptotes.86. f(-1) = −2, ƒ(1) = 2, ƒ(0) = 0, lim ƒ(x) = 1,_lim_ƒ(x) = −1x→ ∞87. lim f(x) = ∞,x+0+lim f(x) = −x→0-00,8个lim f(x) = 1, lim_f(x) = −2∞0+IX--X86. f(−1) = −2, ƒ(1) = 2, ƒ(0) = 0, lim f(x) = 1, _lim_f(x) = −181个

Answered: es Determine lim f(x) and_lim_f(x) for…

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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Question

37-50. Horizontal asymptotes Determine lim f(x) and lim f(x) for the following functions. Then give the horizontal
x →∞
→ ∞
asymptotes of f (if any).
44. f(x) =
=
6x² +1
4x4 + 3x + 1

86-87. Sketching graphs Sketch a possible graph of a function f that satisfies all of the given conditions. Be sure to identify
all vertical and horizontal asymptotes.
86. f(-1) = −2, ƒ(1) = 2, ƒ(0) = 0, lim ƒ(x) = 1,_lim_ƒ(x) = −1
x→ ∞
87. lim f(x) = ∞,
x+0+
lim f(x) = −
x→0
-00,
8个
lim f(x) = 1, lim_f(x) = −2
∞0+I
X--X
86. f(−1) = −2, ƒ(1) = 2, ƒ(0) = 0, lim f(x) = 1, _lim_f(x) = −1
81个

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Introduction:

When a variable approaches its limit from the right, the function's right-hand limit is the value that approaches. When a variable approaches its limit from the left, the function's left-hand limit is the value that approaches.