Question

Using differentials, find the approximate value of $(3.968)^{1/2}$

Find the point on the curve y = x³ – 11x + 5 at which the equation of tangent is y = x – 11.

A problem in mathematics is given to 4 students A, B, C, D. Their chances of solving the problem, respectively, are 1/3, 1/4, 1/5 and 2/3. What is the probability that (i) the problem will be solved ? (ii) at most one of them solve the problem ?

Solve the differential equation : $3e^{x}\tan y\,d x\ +(2-e^{x})\,\mathrm{sec}^{2}\,y\,d y=0,$ given that when x = 0, y = ${\frac{\pi}{4}}.$ 

A speaks truth in 60% of the cases, while B in 90% of cases. In what percent of cases are they likely to contradict each other in stating the same fact ? In the cases of contradiction do you think, the statement of B will carry more weight as he speaks truth in more number of cases than A ?

Find the particular solution of the differential equation : $y e^{y}\,d x=(y^{3}+2x e^{y})d y,y(0)=1$

Find : $\large\textstyle\int$$\large\frac{x^{2}\,d x}{x^{4}+x^{2}-12}\;.$