4 digits

Calculus Level 2

Sam fisher have accomplished a mission. But while leaving the area, he forgot the 4 digit door code. He can't open the door without the 4 digit code.

However, he got some clues:

  • The first digit is 2.

  • The second digit is 022412dx\displaystyle \int^2_0 \dfrac 24 - \dfrac 1 2 dx

  • The third digit is limx2x4x\displaystyle \lim_{x \to \infty} \dfrac{2-x}{4-x}

  • The fourth digit is 220+6\large 2^{2^0} + 6

What is the 4 digit integer?

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