Question
If $y = 5 – 2x,$ show that as $x \rightarrow – 1$ then $y \rightarrow 7$ using tabular method.
✓
Answer
Here, $y = 5 – 2x.$ Taking the values of $x$ very close to $– 1,$ the following table is prepared :
It is clear from the table that when $x$ is brought nearer to $– 1$ by increasing or decreasing its value, the value of $y$ approaches to $7.$
That is, when $x \rightarrow – 1, y \rightarrow 7.$
Hence, it is proved that when $x \rightarrow – 1,$ then $y \rightarrow 7.$
It is clear from the table that when $x$ is brought nearer to $– 1$ by increasing or decreasing its value, the value of $y$ approaches to $7.$
That is, when $x \rightarrow – 1, y \rightarrow 7.$
Hence, it is proved that when $x \rightarrow – 1,$ then $y \rightarrow 7.$
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 value of the following: $\lim _{x \rightarrow k} \frac{x^{2}-\sqrt{x^{2}+3 k^{2}}}{x+k}$
→The monthly production of units in a factory is normally distributed with mean $\mu$ and standard deviation $\sigma$. The $Z-$scores corresponding to the production of $2400$ units and $1800$ units are $1$ and $-0.5$ respectively. Find its mean and standard deviation.
→The sum of squares of differences of ranks for marks in Accountancy and Statistics of $8$ students is obtained $81.5.$ In the observations of marks of Accountancy marks $30$ is repeated thrice and in that Statistics marks $80$ is repeated twice. Find the rank correlation coefficient from this data.
→$\lim _{x \rightarrow 3}\left[\frac{\frac{1}{x^3}-
\frac{1}{27}}{\frac{1}{x}-\frac{1}{3}}\right]$
→\frac{1}{27}}{\frac{1}{x}-\frac{1}{3}}\right]$
The variance of the distribution of a normal variate $X$ is $400 .$ If for some value $x_{1}= 225$ of $X$, the corresponding value of standard normal variate $Z$ is $z_{1}=-1.25$, find the mean of the distribution and $P[210 \leq X \leq 290]$.
→Using the definition, obtain derivative of $y=\frac{1}{a x+b}$.
→The information about six different items used in the production of an electronic item is as follows. Find the Index Number and Interpret it :
| Items | A | B | C | D | E | F |
| Weight | 5 | 10 | 10 | 30 | 20 | 25 |
| Percentage Price Relative | 290 | 315 | 280 | 300 | 315 | 320 |
If $f(x)=3x^{2}+4x+5$ then for which value of x, $f'(x)=f''(x)$ ?
→For which value of $x, f^{\prime \prime \prime}(x)=74$,
if $f(x)=5 x^3-8 x^2-2 x-15$ ?
→if $f(x)=5 x^3-8 x^2-2 x-15$ ?
$3$ bulbs are defective in a box of $10$ bulbs. $2$ bulbs are randomly selected from this box. These bulbs are fixed in two bulb holders installed in a room. Find the probability that the room will be lighted after starting the electric supply. OR Draw Venn diagram for the following events $;(1)$ Mutually exclusive events. $(2)$ Union of events. $(3)$ Intersection of events.
→