Question

Show that a function f : R → R given by f(x) =ax + b,a, b ∈ R, a ≠ 0 is a bijective.

Find : $\large\textstyle\int$$(x+3){\sqrt{3-4x-x^{2}}}\ d x\ .$

Find : $\textstyle\int$${\frac{x^{3}}{x^{4}+3x^{2}+2}}d x~.$

Find the points on the curve y = x³ at which the slope of the tangent is equal to y-coordinate of the point.

Find the equations of tangents to the curve y = (x²– 1) (x – 2) at the points, where the curve cuts the X-axis.

Using differentials, find the approximate value of ${\sqrt{49\cdot5}}\ .$

If A = $\left(\begin{array}{l l l }2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & -1 & 0\end{array}\right)$ , find A² – 5A + 4I and hence find a matrix X such that A² – 5A + 4I + X = 0.