Find the minimum vertical distance between the graphs of

y=x^{\small 2}-4x+6 and y=-x^{\small 2}.

Your answer must be numerical !!!

Find the points on the curve y=x^{\small 2} that are closest to the point (0, 2). 

Enter the value of the y-coordinate of these points.

Your answer must be a numerical value in the decimal form !!!

Find the maximum area of a rectangle that can be inscribed above the x-axis 

and under the graph of y=3-x^{\small 2}.

Your answer must be a numerical value !!!

A rectangular container with a square base and an open top is to have a volume of 4m³. 

Find the smallest possible value of the surface area of such a container.

Your answer must be a numerical value !!!

Evaluate the limit

\lim_{\small x\to 4}\frac{x^{\small 2}+4x}{x^{\small 3}-2x^{\small 2}}

Your answer must be a numerical value!!!

If the limit does not exist or is infinite, enter 100.

Evaluate the limit

\lim_{\small x\to 2^{+}}\frac{x^{\small 2}-4}{x^{\small 2}-4x+4}

Choose the correct answer.

Evaluate the limit

\lim_{\small x\to 0^{+}}\frac{1}{|x|}-\frac{1}{x}

Choose the correct answer.

Apply the intermediate-value theorem to locate a solution of the equation

x^{\small 3}-x=x^{\small 2}-2

Choose the correct interval.

Find the value of the constant c that will make f(x) continuous.

f(x)=\left{\begin{matrix}x^{\small 2}+cx-1&,&x\le 3\\2x+c&,&x>3\end{matrix}\right.

Your answer must be a numerical value !!!

Evaluate the limit

\lim_{\small x\to\infty}\frac{(3x^{\small 2}+1)(2x+1)^{\small 2}}{\left(4x^{\small 2}+x+5\right)^{\small 2}}

Your answer must be a numerical value in the decimal form !!!

If the limit does not exist or is infinite, enter 100.