Evaluate the following limits : _ x -3 [x+3 x^2+4 x+3 ] - Vidyadip

Question

Evaluate the following limits : $\lim _{x \rightarrow-3}\left[\frac{x+3}{x^2+4 x+3}\right]$

✓

Answer

$\lim _{x \rightarrow-3}\left[\frac{x+3}{x^2+4 x+3}\right]$
$=\lim _{x \rightarrow-3} \frac{x+3}{(x+3)(x+1)} \quad \quad \cdots\left[\begin{array}{l} \because x \rightarrow-3, x \neq-3, \\ \therefore x+3 \neq 0 \end{array}\right]$
$=\lim _{x \rightarrow-3} \frac{1}{x+1}$
$=\frac{1}{-3+1}$
$=-\frac{1}{2}$

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 "Solve the following Question.(1 Marks)" from Limits→Limits — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Write the sum of first n even natural numbers.

The given following sets are finite & in which of it infinite in if?
$\{\text{x}\in\text{N}:\text{x}<200\}$

Write the equation of the line passing through the point (1, -2) and cutting off equal intercepts from the axes.

Write the maximum number of points of intersection of 8 straight lines in a plane.

Write the derivative of f(x) = 3|2 + x| at x = -3.

Write the expression ${^\text{n}}\text{C}_{\text{r}+1}+{^\text{n}}\text{C}_{\text{r-1}}+2\times{^\text{n}}\text{C}_{\text{r}-1}$in the simplest form.

If A = {1, 2, 3}, B = {4, 5, 6}, the given following are relations from A to B? Give reason in support of your answer.
{(1, 5), (2, 6), (3, 4), (3, 6)}

Write the negation of the following statements:
p: For every positive real number x, the number (x - 1) is also positive.

If A = {1, 2, 3}, B = {4, 5, 6}, check if the following are relations from A to B. Also, write its domain and range. $R_3=\{(1,4),(1,5),(3,6),(2,6),(3,4)\}$

Find whether the following functions are onto or not.

$f: R \rightarrow R$ defined by $f(x)=x^2+3$ for all $x \in R$