A Polynomial Approximation

★ 6/10calculus Monotonicity Estimation inequality

Problem

1. Prove that for $x \in [0, 1]$ ,

\frac{\sqrt{2}}{2}x \leqslant \sin x \leqslant x.

If the inequality

ax + x^2 + \frac{x^3}{2} + 2(x+2)\cos x \leqslant 4

holds for all $x \in [0, 1]$ , find the range of possible values of the real number $a$ .

Answer

Solution

Difficulty	6/10
Topics	calculus, Monotonicity, Estimation, inequality

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments

No comments yet.