Problem

PART 1: Fill in the blanks.

• Work need not be shown, only answers will be graded.

• 4 points for each blank and 100 points total.

• Each answer need to be clearly labeled on the answer sheet.

• Use of any device with computer algebra system during the exam will result in zero points.

1. Compute the following limits

• $\displaystyle\lim_{x\to 0}\left(\cos x+\frac{1}{2}x^2\right)^{\frac{1}{x^4}}=\underline{\quad(1)\quad}$.
• $\displaystyle\lim_{x\to 0}\frac{3x-\sin 3x}{5x-\tan 5x}=\underline{\quad(2)\quad}$.