Application of ...

The value of \(\sqrt{24.99}\) is:

The value of \(\sqrt{36.01}\) is:

The maximum value of \(\frac{\operatorname{ln} x}{x}\) is:

The radius of a circle is changing at the rate of \(\frac{ dr }{ dt }=0.01\) m/sec. The rate of change of its area \(\frac{ dA }{ dt }\), when the radius of the circle is \(4\) m, is:

If the radius of a sphere is measured as 6 m with an error of 0.02 m, then find the approximate error in calculating its surface area.

Find the minimum value of \(3 x^{4}-8 x^{3}+12 x^{2}-48 x+1\) on the interval \([1,4]\) and \(x \in R\)?

Find slope of the tangent to the curve \(2 x^{3}+3 y=2 y^{3}+3 x\) at \(p(x, y)\).

Find the approximate value of \(f(3.01)\), where \(f(x)=3 x^{2}+3\).

A balloon, which always remains spherical, has a variable diameter \(\frac{3}{2}(4 x +3)\). Find the rate of change of its volume with respect to \(x\).

Find the equation of tangent to the curve \(y=\sqrt{5 x-3}-2\), which is parallel to the line \(4 x-2 y+3=0\)?

If \(f ( x )\) is an increasing function and \(g ( x )\) is a decreasing function such that \(\operatorname{gof}( x )\) is defined, then gof \((x)\) will be:

Find the equation of tangent of \(y=x^{2}\) at \(x=1\)

The interval in which the function \(f(x)=2 x^{3}-15 x^{2}+36 x+12\) is increasing in:

What is the maximum value of \(\sin 2 x \cdot \cos 2x\)?

Find the rate of change of area of the square at the edge length of 12 cm, if the rate of change of edge length of the square is 2 cm/s.

Which of the following is true regarding the function \(f(x)=\log (\sin x)\)?

Which one of the following statements is correct?

Find the equation of the normal to the curve \(y=3 x^{2}+1\), which passes through \((2,13)\).

If the line \(y=4 x+c\) is a tangent to the circle \(x^{2}+y^{2}=9\) then find the value possible values of \(c\)?

What is the approximate value of \((1.04)^{\frac{1}{4}}\)?

The value of \((242)^{1 / 5}\) is.

The maximum value of \(\sin \left(x+\frac{\pi}{6}\right)+\cos \left(x+\frac{\pi}{6}\right)\) in the interval \(\left(0, \frac{\pi}{2}\right)\) is attained at:

For the given curve: \(y=2 x-x^{2}\), when \(x\) increases at the rate of 3 units/sec, then how the slope of curve changes?

Amongst all the pairs of positive numbers with sum 24, find those whose product is maximum?

If \(f(x)=X^{5}-20 X^{3}+240 X\) then \(f'(x)\) is:

Find the interval in which the function \(f(x)=\log (1+x)-\frac{x}{(1+x)}\) is decreasing?

It is given that at \(x=2\), the function \(x^{3}-12 x^{2}+k x-8\) attains its maximum value, on the interval \([0,3]\). Find the value of \(k\).

If at any instant \(t\), for a sphere, \(r\) denotes the radius, \(S\) denotes the surface area and \(V\) denotes the volume, then what is \(\frac{d V}{d t}\) equal to?

Find the points on the curve \(y=x^{2}\) at which the slope of the tangent is equal to the \(y\) coordinate of the point.

The maximum and minimum values of the function |cos 2x + 7| are: