Recent questions tagged sec-1

Prove the following inequalities: $\cos x> 1-\large\frac{x^{2}}{2}, $$x>0$

asked May 4, 2013 by poojasapani_1

1 answer

Find the intervals on which $f$ is increasing or decreasing. $f(x)=\sin^{4}x+\cos^{4}x $ in $ [0 , \large\frac{\pi}{2}]$

asked May 4, 2013 by poojasapani_1

1 answer

Find the intervals on which $f$ is increasing or decreasing. $f(x)=x+\cos x $ in $[0 , \pi ]$

asked May 4, 2013 by poojasapani_1

1 answer

Find the intervals on which $f$ is increasing or decreasing. $f(x)=x-2\sin x,[0 , 2\pi ]$

asked May 4, 2013 by poojasapani_1

1 answer

Find the intervals on which $f$ is increasing or decreasing. $f(x)=x^{3}+x+1$

asked May 4, 2013 by poojasapani_1

1 answer

Find the intervals on which $f$ is increasing or decreasing. $f(x)= x^{3}-3x+1$

asked May 4, 2013 by poojasapani_1

1 answer

Find the intervals on which $f$ is increasing or decreasing. $f(x)=20-x-x^{2}$

asked May 4, 2013 by poojasapani_1

1 answer

Prove that the following functions are not monotonic in the intervals given. $\tan x + \cot x $ on $[0 , \large\frac{\pi}{2}]$

asked May 4, 2013 by poojasapani_1

1 answer

Prove that the following functions are not monotonic in the intervals given. $x \sin x$ on $[0 , \pi ]$

asked May 4, 2013 by poojasapani_1

1 answer

Prove that the following functions are not monotonic in the intervals given. $x(x-1)(x+1) $ on $[0 , 2 ]$

asked May 4, 2013 by poojasapani_1

1 answer

Prove that the following functions are not monotonic in the intervals given. $2x^{2}+x-5$ on $[-1 ,0 ]$

asked May 4, 2013 by poojasapani_1

2 answers

Which of the following function are increasing or decreasing on the interval given? \[\] $x\sin x$ on$ [0 , \large\frac{\pi}{4}]$

asked May 4, 2013 by poojasapani_1

1 answer

Which of the following function are increasing or decreasing on the interval given? \[\]$x(x-1)(x+1) $ on $[-2 , 1 ]$

asked May 4, 2013 by poojasapani_1

1 answer

Which of the following function are increasing or decreasing on the interval given? \[\]$e^{-x} $ on $[0 , 1 ]$

asked May 4, 2013 by poojasapani_1

1 answer

Which of the following function are increasing or decreasing on the interval given? \[\]$2x^{2}+3x$ on $[-\large\frac{1}{2} ,\frac{1}{2}]$

asked May 4, 2013 by poojasapani_1

1 answer

Which of the following function are increasing or decreasing on the interval given? $x^{2}-1 $on$[0 , 1]$

asked May 4, 2013 by poojasapani_1

1 answer

Prove that $\log _e x $ is strictly increasing function on $(0 ,\infty)$.

asked May 4, 2013 by poojasapani_1

1 answer

Prove that $e^{x} $ is strictly increasing function on $R$.

asked May 4, 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

Obtain the Maclaurin's series expansion for:$\;\tan x,- \large\frac{\pi}{2} \lt \normalsize x \lt \large\frac{\pi}{2}$

asked May 4, 2013 by poojasapani_1

1 answer

Obtain the Maclaurin's series expansion for:$\;\large\frac{1}{1+x}$

asked May 4, 2013 by poojasapani_1

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Obtain the Maclaurin's series expansion for:$\;\cos^{2}x$

asked May 4, 2013 by poojasapani_1

1 answer

Obtain the Maclaurin's series expansion for:$\;e^{2x}$

asked May 4, 2013 by poojasapani_1

1 answer

At $2.00$ pm a car's speedometer reads $30$ miles/hr, at $2.10$ pm it reads $50$ miles/hr. Show that sometime between $2.00$ and $2.10$ the acceleration is exactly $120$ miles/hr$^{2}$.

asked May 4, 2013 by poojasapani_1

1 answer

If $f(1)=10$ and $f '(x)\geq 2 $ for $1\leq x \leq 4 $ how small can $f(4)$ possibly be?

asked May 4, 2013 by poojasapani_1

1 answer

Verify Lagrange's theorem for the following function;\[\]$f(x)=x^{3}-5x^{2}-3x\;[1,3]$

asked May 3, 2013 by poojasapani_1

1 answer

Verify Lagrange's theorem for the following function;\[\]$f(x)=x^{\large\frac{2}{3}}[-2,2]$

asked May 3, 2013 by poojasapani_1

1 answer

Verify Lagrange's theorem for the following function;\[\] $f(x)=2x^{3}+x^{2}-x-1\quad [0,2]$

asked May 3, 2013 by poojasapani_1

1 answer

Verify Lagranges theorem for the following function;$f(x)=\large\frac{1}{x}$$\quad[1,2]$

asked May 3, 2013 by poojasapani_1

1 answer

Verify Lagrange's law of mean for the following function;\[\]$f(x)=1-x^{2} \quad [0,3]$.

asked May 3, 2013 by poojasapani_1

1 answer

Using Rolle's theorem find the points on the curve $y=x^{2}+1,-2\leq x \leq 2$ where the tangent is parallel to $x$- axis.

asked May 3, 2013 by poojasapani_1

1 answer

Verify Rolle's theorem for the following function; $f(x)=4x^{3}-9x;-\large\frac{3}{2}\leq x\leq \frac{3}{2}$.

asked May 3, 2013 by poojasapani_1

1 answer

Verify Rolle's theorem for the following functions; $f(x)=|x-1|,0\leq x\leq 2.$

asked May 3, 2013 by poojasapani_1

1 answer

Verify Rolle's theorem for the following function; $f(x)=x^{2}, 0\leq x\leq 1$

asked May 3, 2013 by poojasapani_1

1 answer

Verify Rolle's theorem for the following function; $f(x)=\sin x, 0\leq x\leq\pi$.

asked May 3, 2013 by poojasapani_1

1 answer

If the curve $ y^{2}=x$ and $xy=k$ are orthogonal than prove that $8k^{2}=1.$

asked May 3, 2013 by poojasapani_1

1 answer

Show that the equation of the normal to the curve $x=a\cos^{3}\theta ; y=a\sin^{3}\theta$ at $\;'\theta'$ is$\; x\cos\theta-y\cos\theta=a\cos 2\theta.$

asked May 3, 2013 by poojasapani_1

1 answer

At what angle $\theta $ do the curves $y=a^{x}$ and $y=b^{x}$ intersect $(a{\neq}b)$?

asked May 3, 2013 by poojasapani_1

1 answer

Prove that the curve $2x^{2}+4y^{2}=1$ and $6x^{2}-12y^{2}=1$ cut each other at right angles.

asked May 3, 2013 by poojasapani_1

1 answer

Let $P$ be a point on the curve $y=x^{3}$ and suppose that the tangent line at $P$ intersects the curve again at $Q$. Prove that the slope at $Q$ is four times the slope at $P$.

asked May 3, 2013 by poojasapani_1

1 answer

Find the equations of normal to $y=x^{3}-3x$ that is parallel to $2x+18y-9=0.$

asked May 3, 2013 by poojasapani_1

1 answer

Find the equations of those tangents to the circle $x^{2}+y^{2}=52,$ which are parallel to the straight line $2x+3y=6$.

asked May 3, 2013 by poojasapani_1

1 answer

At what points on the curve $x^{2}+y^{2}-2x-4y+1=0$ the tangent is parallel to $y$- axis.

asked May 3, 2013 by poojasapani_1

1 answer

At what points on the curve $x^{2}+y^{2}-2x-4y+1=0$ the tangent is parallel to $x$- axis.

asked May 3, 2013 by poojasapani_1

1 answer

Find at what points on the circle $x^{2}+y^{2}=13$, the tangent is parallel to the line $2x+3y=7$.

asked May 3, 2013 by poojasapani_1

1 answer

Find the point on curve $x^{2}-y^{2}=2$ at which the slope of the tangent is $2$

asked May 1, 2013 by poojasapani_1

1 answer

Find the equation of the tangent and normal to the curves.$ \;y=\large\frac{1+\sin x}{\cos x}$ at $\;x=\large\frac{\pi}{4}$

asked May 1, 2013 by poojasapani_1

1 answer

Find the equation of the tangent and normal to the curves.$\;y=2\sin^{2} 3x$ at $\;x=\large\frac{\pi}{6}$

asked May 1, 2013 by poojasapani_1

1 answer

Find the equation of the tangent and normal to the curves.$\;y=x-\sin x\cos x, $at$\;x=\large\frac{\pi}{2}$

asked May 1, 2013 by poojasapani_1

1 answer

Find the equation of the tangent and normal to the curves. $y=x^{2}-4x-5$ at $\;x=-2$

asked May 1, 2013 by poojasapani_1

1 answer

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