431-1-2-3á-578/2Find lim f(x) =→7+Find limThe graph of the function f(x) = cot is given above for the interval x = [0, 2π] ONLY.Determine the one-sided limit. Then indicate the equation of the vertical asymptote.+0+*XTThis indicates the equation of a vertical asymptote is =378/2f(x) =+x2nThis indicates the equation of a vertical asymptote is =

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Answered: 5 4 3 1 -1 -2 -3 -4 -5 п/2 П 3п/2 +X 27…

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.FR1: A Further Look: Limits

Problem 3E

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7578 Local Extrema and Asymptotes Draw a graph of the function and use it to determine the asymptotes and the local maximum and minimum values. y=2x2Inx
number 98 in strang and herman calculus 1. Can you provide a full work up as well as an explanation of the steps? I am struggling with finding 0/0 using direct substitution. https://openstax.org/books/calculus-volume-1@24.1/pages/2-3-the-limit-laws 98. limh→01a+h−1ah,limh→01a+h−1ah, where a is a non-zero real-valued constant
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EXAMPLE 3 Evaluate the limit below and indicate which properties of limits are used at each stage. lim x → ∞ 5x2 − 5x − 2/ 4x2 + 3x + 1 SOLUTION As x becomes large, both numerator and denominator become large, so it isn't obvious what happens to their ratio. We need to do some preliminary algebra.To evaluate the limit at infinity of any rational function, we first divide both numerator and denominator by the highest power of x that occurs in the denominator. (We may assume that x ≠ 0, since we are interested only in large values of x.) In this case the highest power of x in the denominator is x2, so we have lim x → ∞ 5x2 − 5x − 2/ 4x2 + 3x + 1 = lim x → ∞ 5x2 − 5x − 2/x2 4x2 + 3x + 1/x2 = lim x → ∞ 5 − 5/x − 2/x2 4 + 3/x + 1/x2 = lim x → ∞ 5 − 5/x − 2/x2 lim x → ∞ 4 + 3/x + 1/x2…
The graph of the function f(x)=cotxf(x)=cotx is given above for the interval x∈[0,2π]x∈[0,2π] ONLY.Determine the one-sided limit. Then indicate the equation of the vertical asymptote.Find limx→π− f(x)=limx→π- f(x)= This indicates the equation of a vertical asymptote is x= .Find limx→0+ f(x)=limx→0+ f(x)= This indicates the equation of a vertical asymptote is x=.
The limit of a function if x approaches some value, a, exists if: a. the function is of the form f(x) = xⁿ where n is a rational number b. two of the other answers are correct c. the function is a polyomial function with NO domain restrictions d. the same value of 'f' is converged upon as x approaches a from both sides of a
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2. a) Suppose f and g are functions with domain R. If both f and g are even but f+g is odd, then prove that g(x) = −f(x) for all x ∈ R. b) Suppose neither limx→0 f(x) nor limx→0 g(x) exists. Show that limx→0 [f(x)g(x)] may exist. c) Suppose f is differentiable everywhere and f'(x) > 0 for all numbers x except for a single number d. Prove that f is always strictly increasing. d) Consider the function f(x) = 4√ x on some closed interval and by applying the Mean Value Theorem, show that3 <4√82 <325/108 e) Prove that limx→4 √x = 2 using the ε-δ-definition. Hint: √x − 2 =x − 4/√x + 2

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5 4 3 1 -1 -2 -3 -4 -5 п/2 П 3п/2 +X 27 Q