csat-suneung 2007 Q26 (Calculus)

csat-suneung · South-Korea · csat__math-science 3 marks Small angle approximation
$\lim _ { x \rightarrow a } \frac { 2 ^ { x } - 1 } { 3 \sin ( x - a ) } = b \ln 2$ is satisfied by two constants $a , b$. What is the value of $a + b$? [3 points]
(1) $\frac { 1 } { 6 }$
(2) $\frac { 1 } { 5 }$
(3) $\frac { 1 } { 4 }$
(4) $\frac { 1 } { 3 }$
(5) $\frac { 1 } { 2 }$
$\lim _ { x \rightarrow a } \frac { 2 ^ { x } - 1 } { 3 \sin ( x - a ) } = b \ln 2$ is satisfied by two constants $a , b$. What is the value of $a + b$? [3 points]\\
(1) $\frac { 1 } { 6 }$\\
(2) $\frac { 1 } { 5 }$\\
(3) $\frac { 1 } { 4 }$\\
(4) $\frac { 1 } { 3 }$\\
(5) $\frac { 1 } { 2 }$