remains unchanged
decreases
With the rise in temperature, the Young’s modulus of elasticity generally decreases. This is because materials tend to expand and become less stiff when heated, leading to a decrease in the material’s elasticity. Therefore, the correct answer is Option 4: decreases.
If the given graph shows the load (W) attached to and the elongation ($\Delta l$) produced in a wire of length 1 meter and cross-sectional area 1 mm$^2$, then the Young's modulus of the material of the wire is
Let $ f: \mathbb{R} \to \mathbb{R} $ be a twice differentiable function such that $$ f''(x)\sin\left(\frac{x}{2}\right) + f'(2x - 2y) = (\cos x)\sin(y + 2x) + f(2x - 2y) $$ for all $ x, y \in \mathbb{R} $. If $ f(0) = 1 $, then the value of $ 24f^{(4)}\left(\frac{5\pi}{3}\right) $ is: