Recent questions tagged sec8

Examine if Rolle’s theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle’s theorem from these example? $(iii)\;f (x) = x^2 - 1 \; for\; x \: \in [1,2] $

asked Aug 16, 2013 by sreemathi.v

1 answer

Examine if Rolle’s theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle’s theorem from these example? $ (ii)\;f (x) = [x] \; for\; x \: \in [-2,2]$

asked Aug 16, 2013 by sreemathi.v

1 answer

Examine the applicability of Mean Value Theorem for all three functions given in $(iii)\;f (x) = x^2-1 \;for\; x \: \in [1,2]$

asked May 13, 2013 by sreemathi.v

1 answer

Examine the applicability of Mean Value Theorem for all three functions given in $(ii)\;f (x) = [x] \;for\; x \: \in [-2,2]$

asked May 13, 2013 by sreemathi.v

1 answer

Evaluate the definite integral as limits of sums $\displaystyle\int\limits_a^bx\;dx$

asked Dec 4, 2012 by sreemathi.v

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Evaluate the definite integral as limits of sums $\displaystyle\int\limits_0^5(x+1)dx$

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral as limits of sums $\begin{align}\int\limits_2^3x^2dx \end{align}$

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral as limits of sums\[\int\limits_1^4(x^2-x)dx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral as limits of sums\[\int\limits_{-1}^1e^xdx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral as limits of sums $\displaystyle\int\limits_0^4(x+e^{2x})dx$

asked Dec 4, 2012 by sreemathi.v

1 answer

Examine the applicability of Mean Value Theorem for all three functions given in $(i)\;f (x) = [x] \;for\; x \: \in [5,9]$

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Verify Mean Value Theorem, if $ f (x) = x^3 - 5x^2 - 3x $ in the interval $ [a,b]$, where $ a = 1$ and $ b = 3$. Find all $ c \in (1,3) $ for which $ f'(c) = 0$.

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Verify Mean Value Theorem, if $ f (x) = x^2 - 4x - 3 $ in the interval $ [a,b]$, where $ a = 1 $ and $b = 4 $.

asked Nov 21, 2012 by thanvigandhi_1

1 answer

If $ f : [ -5,5] \rightarrow R $ is a differentiable function and if $ f' (x) $ does not vanish anywhere, then prove that $ f (-5) \: \neq \: f (5)$.

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Examine if Rolle's theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle's theorem from these example? $(i)\;f (x) = [x] \;for\; x \: \in [5,9] $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Verify Rolle's theorem for the function $ f (x) =x^2 + 2x - 8, x \: \in [ -4 , 2 ]. $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

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Examine if Rolle’s theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle’s theorem from these example? $(iii)\;f (x) = x^2 - 1 \; for\; x \: \in [1,2] $

Examine if Rolle’s theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle’s theorem from these example? $ (ii)\;f (x) = [x] \; for\; x \: \in [-2,2]$

Examine the applicability of Mean Value Theorem for all three functions given in $(iii)\;f (x) = x^2-1 \;for\; x \: \in [1,2]$

Examine the applicability of Mean Value Theorem for all three functions given in $(ii)\;f (x) = [x] \;for\; x \: \in [-2,2]$

Evaluate the definite integral as limits of sums $\displaystyle\int\limits_a^bx\;dx$

Evaluate the definite integral as limits of sums $\displaystyle\int\limits_0^5(x+1)dx$

Evaluate the definite integral as limits of sums $\begin{align}\int\limits_2^3x^2dx \end{align}$

Evaluate the definite integral as limits of sums\[\int\limits_1^4(x^2-x)dx\]

Evaluate the definite integral as limits of sums\[\int\limits_{-1}^1e^xdx\]

Evaluate the definite integral as limits of sums $\displaystyle\int\limits_0^4(x+e^{2x})dx$

Examine the applicability of Mean Value Theorem for all three functions given in $(i)\;f (x) = [x] \;for\; x \: \in [5,9]$

Verify Mean Value Theorem, if \( f (x) = x^3 - 5x^2 - 3x \) in the interval \( [a,b]\), where \( a = 1\) and \( b = 3\). Find all \( c \in (1,3) \) for which \( f'(c) = 0\).

Verify Mean Value Theorem, if \( f (x) = x^2 - 4x - 3 \) in the interval \( [a,b]\), where \( a = 1 \) and \(b = 4 \).

If \( f : [ -5,5] \rightarrow R \) is a differentiable function and if \( f' (x) \) does not vanish anywhere, then prove that \( f (-5) \: \neq \: f (5)\).

Examine if Rolle's theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle's theorem from these example? $(i)\;f (x) = [x] \;for\; x \: \in [5,9] $

Verify Rolle's theorem for the function \( f (x) =x^2 + 2x - 8, x \: \in [ -4 , 2 ]. \)