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Recent questions tagged p15

Verify the Rolles Theorem for the function $ f(x)=\sin x- \cos x, $in the interval $ \bigg[\Large\frac{\pi}{4},\frac{5\pi}{4}\bigg]$

asked Jan 28, 2013 by meena.p

1 answer

Using LMV Theorem, find a point on the curve $ y=(x-3)^2,$ where the tangent is parallel to the chord joining (3,0) and (5,4).

asked Jan 28, 2013 by meena.p

1 answer

If f(x) and g(x) are functions derivable in [a,b] such that f(a) = 4, f(b) = 10, g(a) =1, g(b) =3.Show that for a < c < b, we have $ f'(c)=3g'(c).$

asked Jan 28, 2013 by meena.p

1 answer

It is given that for the function $ f(x)=x^3-6x^2+px+q\;on\;[1,3].$Rolles theorem holds with $ c=2+\large\frac{1}{\sqrt 3}.$Find the values of p and q.

asked Jan 28, 2013 by meena.p

1 answer

Let $f :[0,1]\rightarrow[0,1]$ be defined by$$ f(x)= \left \{ \begin{array}{1 1}\;x,if\;x\;is\;rational & \;\\1-x,if\;x\;is\;irrational & \;\end{array} \right.$$ Then $(f o f)x$ is $$\begin{array}{1 1}(A)\;constant & (B)\;1+x\\(C)\;x & (D)\;none\;of\;these\end{array}$$

asked Dec 19, 2012 by sreemathi.v

1 answer

Let $f:R-\{\frac{3}{5}\}\rightarrow R$ be defined by $f(x)=\Large {\frac{3x+2}{5x-3}}$ .Then

asked Dec 19, 2012 by sreemathi.v

1 answer

Let $f:A\rightarrow B\;and\;g:B\rightarrow C$ be the bijective functions.Then $(g\;o\;f)^{-1}$ is

asked Dec 19, 2012 by sreemathi.v

1 answer

Let f:$R\rightarrow R$ be the functions defined by $f(x)=x^3+5.$ Then $f^{-1}(x)$ is

asked Dec 19, 2012 by sreemathi.v

1 answer

Which of the following functions from Z into Z are bijections?\begin{array}{1 1}(A)\;f(x)=x^3 & (B)\;f(x)=x+2\\(C)\;f(x)=2x+1 & (D)\;f(x)=x^2+1\end{array}

asked Dec 19, 2012 by sreemathi.v

1 answer

Let $f:R\rightarrow R $ be defined by $f(x)=3x^2-5\; and \;g:R\rightarrow R \;by \;g(x)=\Large {\frac{x}{x^2+1}}$.Then g o f is

asked Dec 19, 2012 by sreemathi.v

1 answer

Let $f\;:\;R\rightarrow R$ be defined by $f(x)\;=\;\frac{1}{x}\quad x\;\in\; R.$Then f is

asked Dec 19, 2012 by sreemathi.v

1 answer

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