Essential Calculus
2nd Edition
ISBN: 9781285209067
Author: Stewart
Publisher: Cengage
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Students have asked these similar questions
x2 − 1
?. (a) Evaluate Lim _____________
x→1 x2 + 5x − 6
Let
f(x)=x2−2x−35
x−7.
Find a) limf(x)=....,
x→7
Simplify your answer.
b) lim f(x)=...
x→0
Simplify your answer.
and c) lim f(x)=....
x→−5
Simplify your answer.
determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
If
lim x→7 g(x) = 0
and
lim x→7 f(x)/g(x) = 0
exists, then
lim x→7 f(x) = 0.
True. If lim x→7 f(x) is not equal to zero and lim x→7 g(x) = 0, then lim x→7 f(x)/g(x) does not exist.
True. Any number divided by zero is equal to zero.
False. Let g(x) = (x − 7) and f(x) = (x − 1)(x − 7). Then lim x→7 g(x) = 0 and lim x→7 f(x)/g(x) = 0 exists, but lim x→7 f(x) is not equal to 0.
False. Divison by zero is not allowed.
False. There is not enough information given to determine lim x→7 f(x)/g(x)
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- Find the value of lim x→-2π/3 sec(x+3π/2)-3.arrow_forwardGiven lim (4x-3) as x approaches 1. Use the definition of a limt to find a number delta such that the absolute value of x-a is less than delta when the absolute value of f(x)-L is less than 0.08arrow_forwardLet f(x)= {x2+4sec(pix) if 5/3 ≤ x < 3 , -2x+7 if x>3 a. Find lim f(x) and lim f(x) x→3+ x→3−b. Find lim f(x) or explain why it does not exist.arrow_forward
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Limits and Continuity; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=9brk313DjV8;License: Standard YouTube License, CC-BY