csat-suneung 2010 Q28

csat-suneung · South-Korea · csat__math-science 3 marks Tangents, normals and gradients Common tangent line to two curves

[Calculus] The tangent line to the curve $y = e ^ { x }$ at the point $( 1 , e )$ is tangent to the curve $y = 2 \sqrt { x - k }$. What is the value of the real number $k$? [3 points]
(1) $\frac { 1 } { e }$
(2) $\frac { 1 } { e ^ { 2 } }$
(3) $\frac { 1 } { e ^ { 4 } }$
(4) $\frac { 1 } { 1 + e }$
(5) $\frac { 1 } { 1 + e ^ { 2 } }$

[Calculus] The tangent line to the curve $y = e ^ { x }$ at the point $( 1 , e )$ is tangent to the curve $y = 2 \sqrt { x - k }$. What is the value of the real number $k$? [3 points]\\
(1) $\frac { 1 } { e }$\\
(2) $\frac { 1 } { e ^ { 2 } }$\\
(3) $\frac { 1 } { e ^ { 4 } }$\\
(4) $\frac { 1 } { 1 + e }$\\
(5) $\frac { 1 } { 1 + e ^ { 2 } }$

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q26 Q26b Q26c Q27 Q27b Q28 Q28b Q29 Q29b Q30 Q30b