Question

Which of the following is correct answer for the choice of $\alpha$, $\beta$ and $\gamma$ (FINITE) so that $\lim_{y \to 0} \frac{e^{2y} + \alpha - (\beta + 1)y}{y^2} = \gamma$ A) $\alpha = -1$, $\beta = 3$ and $\gamma = 1/2$ B) $\alpha = -1$, $\beta = 1$ and $\gamma = 2$ C) $\alpha = -1$, $\beta = 1$ and $\gamma = 1/2$ D) $\alpha = 1$, $\beta = -3$ and $\gamma = -2$ E) $\alpha = 1$, $\beta = -3$ and $\gamma = 1/2$

          Which of the following is correct answer for the choice of $\alpha$, $\beta$ and $\gamma$ (FINITE) so that
$\lim_{y \to 0} \frac{e^{2y} + \alpha - (\beta + 1)y}{y^2} = \gamma$
A) $\alpha = -1$, $\beta = 3$ and $\gamma = 1/2$
B) $\alpha = -1$, $\beta = 1$ and $\gamma = 2$
C) $\alpha = -1$, $\beta = 1$ and $\gamma = 1/2$
D) $\alpha = 1$, $\beta = -3$ and $\gamma = -2$
E) $\alpha = 1$, $\beta = -3$ and $\gamma = 1/2$
        
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Which of the following is correct answer for the choice of α, β and γ (FINITE) so that
limy → 0(e^2y + α - (β + 1)y)/(y^2) = γ
A) α = -1, β = 3 and γ = 1/2
B) α = -1, β = 1 and γ = 2
C) α = -1, β = 1 and γ = 1/2
D) α = 1, β = -3 and γ = -2
E) α = 1, β = -3 and γ = 1/2

Added by Elena H.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Which of the following is the correct answer for the choice of a, 3, and √(FINITE) so that lim y→0 √(y^2) A) a = -1, 3 = 3 and √(FINITE) = 1/2 B) a = -1, 3 = 1 and √(FINITE) = 2 C) a = -1, √(FINITE) = 1 and √(FINITE) = 1/2 D) a = 1, 3 = -3 and √(FINITE) = -2 E) a = 1, 3 = -3 and √(FINITE) = 1/2
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Transcript

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00:01 Hi, now we are going to find which of the following are true.
00:04 Now in option a, the given statement is limit s tends to 1, 2 s squared plus s minus 3 divide by s minus 1 is equal to minus 1.
00:20 Now 2 s squared plus s minus 3 divide by s minus 1 can be written as 2 s plus 3.
00:31 Into s minus 1 whole divide by s minus 1 and it will be equal to 2 s plus 3 then the given limit s tends to 1 2 s squared plus s minus 3 divided by s minus 1 is equal to limit s tends to 1 to 1 2 s plus 3 and it will be equal to 2 into 1 plus 3 that is 5 but the given answer is minus 1 so this is a false statement and next in option b the given statement is limit x tends to 2 x minus 2 divide by modulus of x minus 2 does not exist now we have limit x tends to 2 minus x minus 2 divide by models of x minus 2 is equal minus 1 and limit x tends to 2 plus x minus 2 divide by modulus of x minus 2 is equal to plus 1.
01:50 So here we have limit x tends to 2 minus x minus 2 divide by models of x minus 2 is not equal to limit x tends to 2 plus x minus 2 divide by models of x minus 2.
02:07 Minus 2.
02:08 So the limit does not exist.
02:17 Therefore the given statement is true...
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