Examine the function for continuity. f(x)=1 x-5 , x 5 - Vidyadip

Question

Examine the function for continuity.
$f(x)=\frac{1}{x-5}$, x $\neq$ 5

✓

Answer

The given function is $f(x)=\frac{1}{x-5}, x \neq 5$
For any real number $k \neq 5$ we get,
$\lim _{x \rightarrow k} f(x)=\lim _{x \rightarrow k} \frac{1}{(x-5)}=\frac{1}{(k-5)}$
Also, $f(k)=\frac{1}{(k-5)}(As, ~~ k \neq 5)$
Thus, $\mathop {\lim }\limits_{{{x}} \to {{k}}} {{f}}({{x}}) = {{f}}({{k}})$
Therefore, f is continuous at every point in the domain of f and thus, it is a continuous function.

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 "1 Marks Question" from Continuity and Differentiability→Continuity and Differentiability — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Construct a $3 \times 4$ matrix $A = [a_{ij}]$ whose element $a_{ij}$ are given by: $a_{ij} = 2i$

Determine order and degree $($if defined$)$ of differential equations given in Exercise.
$(y''')^2 + (y")^3 + (y')^4 + y^5 = 0$

A water tank has the shape of an inverted right circular cone with its axis vertical and vertex lower most. Its semi vertical angle is $\tan^{-1}(0.5)$ water is poured into it at a constant rate of $5$ cubic metre per hour. Find the rate at which the level of the water is rising at the instant when the depth of water in the tank is $4 \ m$.

If $\left[\begin{array}{cc}\lambda-4 & -3 \\ 1 & 6-\lambda\end{array}\right]=\left[\begin{array}{ll}a & -3 \\ 1 & -4\end{array}\right]$, then find the value of $a$.

Write the equation of a plane which is at a distance of $5\sqrt{3}$ units from origin and the normal to which is equally inclined to coordinate axes.

Find the principal value of $\sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right)$

If $\overrightarrow{\text{a}}$and$\overrightarrow{\text{b}}$ are two unit vectors such that $\overrightarrow{\text{a}}$+ $\overrightarrow{\text{b}}$is also a unit vector, then find the angle between $\overrightarrow{\text{a}}$and $\overrightarrow{\text{b}}$.

Integrate the function: $\int \frac{1}{\sqrt{x+a}+\sqrt{x+b}} d x$

The two vectors $\hat{\text{j}} + \hat{\text{k}}$ and $3\hat{\text{i}} - \hat{\text{j}} + 4\hat{\text{k}}$ represent the two sides AB and AC, respectively of a $\triangle \text{ABC},$ Find the length of the median through A.

Evaluate the following integrals:
$\int\log_\text{x}\text{xdx}$