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Unformatted text preview: ope 2, and it passes the point (2, −3), by the pointslope formula, the tangent line equation is y + 3 = 2(x − 2). That is, y = 2x − 7.
1 2. Find limx→0 x2 esin( x ) by using the Squeeze Theorem.
Since the range of sine is always between −1 and 1,
1
−1 ≤ sin( ) ≤ 1.
x
Now, since y = ex is an increasing function, this inequality implies that
1 e−1 ≤ esin( x ) ≤ e1 ,
and by multiplying x2 ≥ 0 to each term above, we get
1 x2 e−1 ≤ x2 esin( x ) ≤ x2 e1 .
Hence, since
lim x2 e−1 = 0 = lim x2 e1 , x→ 0 x→ 0 1 by the Squeeze Theorem, it follows that lim...
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This note was uploaded on 02/10/2014 for the course MATH 235 taught by Professor Lucas during the Fall '08 term at James Madison University.
 Fall '08
 LUCAS
 Calculus, Logic, Slope

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