Application of ...

The function $$\frac{ln(1+x)}{x}$$ in $$(0,\infty )$$ is

If the subnormal to the curve $${ x }^{ 2 }.{ y }^{ n }={ a }^{ 2 }$$ is a constant then n=

Let $$f(x)$$ be a function satisfying $$f'(x)=f(x)$$ with $$f(0)=1$$ and g be the function satisfying $$f(x)+g(x)=x^2$$ the value of the integral $$\displaystyle\int^1_0f(x)g(x)dx$$ is?

Define $$f(x) = \dfrac{1}{2} [ |\sin x| + \sin x], 0 < x \le 2\pi$$. The $$f$$ is

Let N be the set of positive integers. For all $$n \in N$$, let
$$f_n = (n + 1)^{1/3} - n^{1/3}$$ and $$A = \left\{n \in N : f_{n +1} < \dfrac{1}{3(n + 1)^{2/3}} < f_n \right\}$$
Then

A Stationary point of $$f(x)=\sqrt{16-x^{2}}$$  is 

If $$\int { \dfrac { { 2x }^{ 2 } }{ \left( { x }^{ 2 }+1 \right) ^{ 2 } } } dx=f\left( x \right) +c$$ where f (0) = 0, then

$$A\;sationary\;po\operatorname{int} \;of\;f\left( x \right) = \sqrt {16 - {x^2}} \;is$$

The slope of the tangent to the curve at a point (x, y) on it is proportional to (x-2). If the slope of the tangent to the curve at  (10,-9) on it -3. The equation of the curve is

$$N$$ characters of information are held on magnetic tape, in batches of $$x$$ characters each, the batch processing time is $$\alpha +\beta x^2$$ seconds. $$\alpha $$ and $$\beta $$ are constants. The optical value of $$x$$ for last processing is,