Download App

Mean Value Theorems — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMean Value Theorems3 Marks
Question
Show that the Lagrange's mean value theorem is not applicable to the function
$\text{f}(\text{x})=\frac{1}{\text{x}}\text{ on }[-1,1]$
✓

Answer

Given,
$\text{f}(\text{x})=\frac{1}{\text{x}}$
Clearly, f(x) is does not exist for x = 0
Thus, the given function is discontinuous on [-1, 1]
Hence, Lagrange's mean value theorem is not applicable for the given function on [-1, 1].

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks" from Mean Value Theorems→Mean Value Theorems — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Integrate the function $\frac{1}{\sqrt{x^{2}+2 x+2}}$ 
→
If $|\vec{\text{a}}|=\text{a}$ and $\big|\vec{\text{b}}\big|=\text{b},$ prove that $\Big(\frac{\vec{\text{a}}}{\text{a}^2}-\frac{\vec{\text{b}}}{\text{b}^2}\Big)^2=\Big(\frac{\vec{\text{a}}-\vec{\text{b}}}{\text{ab}}\Big)^2.$
→
Evaluate the following integrals:

$\int\sqrt{\text{cosec}\text{x}-1}\text{ dx}$

→
A vector makes an angle of $\frac{\pi}4$ with each of x-axis and y-axis. Find the angle made by it with the z-axis.
→
Write the minors and cofactors of element of the first column of the following matrices and hence evaluate the determinant in case:
$\text{A}=\begin{vmatrix}-1&4\\2&3 \end{vmatrix}$
→
Solve the following differential equation:

$\frac{dy}{dx} + 2y = \text6 {e^{x}}$

→
Evaluate the following integrals:
$\int\limits^{\frac{\pi}{2}}_{\frac{-\pi}{2}}\log\Big(\frac{2-\sin\text{x}}{2+\sin\text{x}}\Big)\text{dx}$
→
Prove that the function f : N → N, defined by f(x) = x2 + x + 1 is one-one but not onto. Find inverse of f : N → S, where S is range of f.
→
Let f be a real function given by $\text{f(x)}=\sqrt{\text{x}-2}.$ Find the following:
fofof
Also, show that fof ≠ f2.
→
Reduce the equation 2x - 3y - 6z = 14 to the normal form and, hence, find the length of the perpendicular from the origin to the plane. Also, find the direction cosines of the normal to the plane.
→