csat-suneung 2015 Q30

csat-suneung · South-Korea · csat__math-B 4 marks Differentiating Transcendental Functions Regularity and smoothness of transcendental functions

For the function $f ( x ) = e ^ { x + 1 } - 1$ and a natural number $n$, let the function $g ( x )$ be defined as $$g ( x ) = 100 | f ( x ) | - \sum _ { k = 1 } ^ { n } \left| f \left( x ^ { k } \right) \right|$$ Find the sum of all natural numbers $n$ such that $g ( x )$ is differentiable on the entire set of real numbers. [4 points]

For the function $f ( x ) = e ^ { x + 1 } - 1$ and a natural number $n$, let the function $g ( x )$ be defined as
$$g ( x ) = 100 | f ( x ) | - \sum _ { k = 1 } ^ { n } \left| f \left( x ^ { k } \right) \right|$$
Find the sum of all natural numbers $n$ such that $g ( x )$ is differentiable on the entire set of real numbers. [4 points]

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q24 Q25 Q26 Q27 Q28 Q29 Q30