Recent questions tagged p34

Evaluate the limit for the following if exists. $\;\lim \limits_{x \to 1 } x^{\large\frac{1}{x-1}}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to 0+} x^{2}\log_{e}x.$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to 0} \large\frac{\cot x}{\cot 2x}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to \infty} \large\frac{\log _{e}x}{x}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to \infty} \large\frac{\frac{1}{x^{2}}-\large 2\tan^{-1}(\frac{1}{x})}{\Large\frac{1}{x}}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to \infty}\large\frac{\sin\frac{2}{x}}{\Large\frac{1}{x}}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to 2}\large\frac{x^{n}-2^{n}}{x-2}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to 0}\large\frac{\sin ^{-1} x}{x}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to 0} \large\frac{\tan x-x}{x- \sin x}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists.$\;\lim\limits_{x\to 2} \large\frac{\sin \pi x}{2 - x}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists,$\;\lim\limits_{x \to 2} \large\frac{\sin\pi x}{2-x}$

asked May 4, 2013 by poojasapani_1

1 answer

Newtons law of cooling states that the rate of change of the temperature T of an object is proportional to the difference between T and the (constant) temperature t of the surrounding medium. We can write it as \[\frac{dT}{dt}=-K(T-t),K>0\; constant.\]A cup of coffee is served at $ 185^\circ F$ in a room where the temperature is $65^\circ F .$ Two minutes later the temperature of the coffee has dropped to $155^\circ F.$(log 3/4=0.144, log3 = 1.09872). Find the time required for coffee to have $105^\circ F$ temperature.

asked Feb 4, 2013 by meena.p

0 answers

A curve passing through the point (1,1) has the property that the perpendicular distance of the origin from the normal at any point P of the curve is equal to the distance of p from the x-axis. Determine the equation of the curve.

asked Feb 4, 2013 by meena.p

0 answers

The surface area of a balloon being inflated, changes at a rate proportional to time t. If initially its radius is 1 unit and after 3 seconds it is 2 units, find the radius after time 't'.

asked Feb 4, 2013 by meena.p

1 answer

A wet porous substance in the open air losses its moisture at a rate proportional to the moisture content. If a sheet hung in the wind loses half of its moisture during the first hour, when will it have lost 95% moisture, weather conditions remaining the same.

asked Feb 4, 2013 by meena.p

0 answers

A population grows at the rate of 8% per year. How long does it take for the population to double?

asked Feb 4, 2013 by meena.p

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When the interest is compounded continuously, the amount of money invested increases at a rate proportional to its size. If Rs.1000 is invested at 10% compounded continuously, in how many years will the original investment double itself?

asked Feb 4, 2013 by meena.p

0 answers

Solve: \[\frac{xdx+ydy}{xdy-ydx}=\sqrt{\frac{a^2-x^2-y^2}{x^2+y^2}}\] (Hint : take $ x=r\cos \theta,y=r \sin \theta,$ so that $x^2+y^2=r^2)$

asked Feb 4, 2013 by meena.p

0 answers

Solve:\[\frac{dy}{dx}=\frac{x^2+y^2+1}{2xy},\;where\; y(1)=1\]

asked Feb 4, 2013 by meena.p

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Solve:\[(x^3-3xy^2)dx=(y^3-3x^2y)dy\]

asked Feb 4, 2013 by meena.p

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Solve:\[\frac{dy}{dx}=\frac{y^2+y+1}{x^2+x+1}=0.\]

asked Feb 4, 2013 by meena.p

0 answers

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