Question
If $\text{f(x)}=\begin{cases}2\text{x}+3, & \text{x} \le0\\3(\text{x}+1), &\text{x} > 0\end{cases}$Find $\lim\limits_{\text{x}\rightarrow0}\text{f(x)}$ and $\lim\limits_{\text{x}\rightarrow1}\text{f(x)}.$
✓
Answer
$\lim\limits_{\text{x}\rightarrow0^+}\text{f(x)}=\lim\limits_{\text{x}\rightarrow0^+}3\text{(x}+1)=3$
And,
$\lim\limits_{\text{x}\rightarrow0^-}\text{f(x)}=\lim\limits_{\text{x}\rightarrow0^-}2\text{(x)}+3=3$
$\therefore\ \lim\limits_{\text{x}\rightarrow0}\text{f(x)}=3$
$\lim\limits_{\text{x}\rightarrow1}\text{f(x)}=\lim\limits_{\text{x}\rightarrow1}3(\text{x}+1)=3+3=6$
$\therefore\ \lim\limits_{\text{x}\rightarrow1}\text{f(x)}=6$
And,
$\lim\limits_{\text{x}\rightarrow0^-}\text{f(x)}=\lim\limits_{\text{x}\rightarrow0^-}2\text{(x)}+3=3$
$\therefore\ \lim\limits_{\text{x}\rightarrow0}\text{f(x)}=3$
$\lim\limits_{\text{x}\rightarrow1}\text{f(x)}=\lim\limits_{\text{x}\rightarrow1}3(\text{x}+1)=3+3=6$
$\therefore\ \lim\limits_{\text{x}\rightarrow1}\text{f(x)}=6$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the coordinates of the foci, the vertices, the lengths of major and minor axes and the eccentricity of the ellipse $9x^2 + 4y^2 = 36.$
→Decide among the following sets which sets are subsets of each another:
A = {X : X $\in$ R} and x satisfies x2 - 8x + 12 = 0}, B = {2, 4, 6} , C = {2, 4, 6, 8, ...}, D = {6}
→A = {X : X $\in$ R} and x satisfies x2 - 8x + 12 = 0}, B = {2, 4, 6} , C = {2, 4, 6, 8, ...}, D = {6}
Find the equation of a straight line passing through the point of intersection of $x + 2y + 3 = 0$ and $3x + 4y + 7 = 0$ and perpendicular to the straight line $x - y + 9 = 0.$
→A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = $\{$(x, y): the difference between x and y is odd, $\text{x}\in\text{A},\text{y}\in\text{B}\}$ Write R in Roster form.
→In a group of 950 person, 750 can speak Hindi and 460 can speak English. Find:
how many can speak both Hindi and English.
how many can speak both Hindi and English.
The value of $\cos(36^\circ-\text{A})\cos(36^\circ+\text{A})+\cos(54^\circ+\text{A})\cos(54^\circ-\text{A})$ is:
→To receive Grade 'A', in a course, one must obtain an average of 90 marks or more in five examinations (each of 100 marks). If Sunita's marks in first four examinations are 87, 92, 94. and 95, find minimum marks that Sunita must obtain in fifth examination to get Grade 'A' in the course.
The vertices of the triangle are $A(5, 4, 6), B(1, -1, 3)$ and $C(4, 3, 2)$.The intenal bisector of angle $A$ meets $BC$ at $ D.$ Find the coordinates of $D$ and the length $AD.$
→If the coefficients of $(2r + 1)$th and $(r + 2)$th teram in the expansion of $(1 + x)^{43}$ are equal, find r.
→Let A = {1, 2, 3} and B = {3, 4}. Find A × B and show it graphically.