The approximate value of the function $f(x) = x^{3} - 3x + 5$ at $x = 1.99$ is

Let $y = f(x) = 2x^{2} - 3x + 2$. The differential of $y$ when $x$ changes from $2$ to $1.99$ is

$A$ point on the hypotenuse of a triangle is at distances $a$ and $b$ from the sides of the triangle. Show that the minimum length of the hypotenuse is $(a^{\frac{2}{3}}+b^{\frac{2}{3}})^{\frac{3}{2}}$.

The semi-vertical angle of a right circular cone is $45^{\circ}$. If the radius of the base of the cone is measured as $14 \text{ cm}$ with an error of $\left(\frac{\sqrt{2}-1}{11}\right) \text{ cm}$,then the approximate error in measuring its total surface area is (in $\text{sq. cm}$):

The approximate value of $y=(1.01)^3+2(1.01)^{\frac{3}{2}}+5$ is

The approximate value of $x^3-2x^2+3x+2$ at $x=2.01$ is