Mathematics Tes...

Find the area of the region bounded by the parabola \(x^2=4 y, y=2\) and \(y=4\) and the \(y\)-axis in the first quadrant.

Solve: |x – 1| ≤ 5, |x| ≥ 2

Find \(\lim _{\mathrm{x} \rightarrow 1} \frac{\sqrt{\mathrm{f}(\mathrm{x})}-1}{\mathrm{x}-1}\), if \(\mathrm{f}(1)=1\) and \(\mathrm{f^\prime}(1)=3\).

Let \(Z\) be the set of integers. If \(A=\left\{x \in Z: 2^{(x+2)\left(x^{2}-5 x+6\right)}=1\right\}\) and \(B=\{x \in Z:-3<2 x-1<9\},\) then the number of subsets of the set \(A \times B,\) is.

Find the number of terms in \((\sqrt{3}+1)^{8}\):

What is the equation of the ellipse having foci \((\pm 2,0)\) and the eccentricity \(\frac{1 }{ 2}\)?

What is the value of (A - B) ∩ (B - A)?

If \(A=\left[\begin{array}{ccc}2 & x-3 & x-2 \\ 3 & -2 & -1 \\ 4 & -1 & -5\end{array}\right]\) is a symmetric matrix then \(x\):

The equation of the line passing through the point \((2,3)\) with slope \(2\) is