Question
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{3^{2+\text{x}}-9}{\text{x}}$

Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{3^{2+\text{x}}-9}{\text{x}}=\lim\limits_{\text{x}\rightarrow0}\frac{3^2.3^\text{x}-9}{\text{x}}$
$=9\lim\limits_{\text{x}\rightarrow0}\frac{3^\text{x}-1}{\text{x}}$
$=9 \text{log}_\text{e}3$

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

Similar questions

Solve the following quadratic equations:

$x^2-4 x+13=0$

Find x in the following.
$\frac{1}{6!}+\frac{1}{7!}=\frac{\text{x}}{8!}$
Evaluate the following limit:
$\lim\limits_{{\text{x}}\rightarrow\frac{\pi}{2}}\frac{\text{a}^{\cot\text{x}}-\text{a}^{\cos\text{x}}}{\cot\text{x}-\cos\text{x}}$
If the $n^{th}$​​​​​​​ term $a_n​​​​​​​$​​​​​​​ of sequence is given by $\text{a}_\text{n}=\text{n}^2-6\text{n}^2-\text{n}+1,$ write down its first five terms.
An urn contains 4 black, 5 white, and 6 red balls. Two balls are drawn one after the other without replacement. What is the probability that at least one of them is black?
Find composite of f and g:

f = {(1, 1), (2, 4), (3, 4), (4, 3)}
g = {(1, 1), (3, 27), (4, 64)}

Suppose that five good fuses and two defective ones have been mixed up. To find the defective fuses, we test them one-by-one, at random and without replacement What is the probability that we are lucky and find both of the defective fuses in the first two tests?
Show the following quadratic equation by factorization method:
$5x^2 + 6x + 2 = 0$
Find $x, y, z$ if $\left\{\left[\begin{array}{ll}0 & 1 \\ 1 & 0 \\ 1 & 1\end{array}\right]-3\left[\begin{array}{cc}2 & 1 \\ 3 & -2 \\ 1 & 3\end{array}\right]\right\}\left[\begin{array}{l}2 \\ 1\end{array}\right]=\left[\begin{array}{c}x-1 \\ y+1 \\ 2 z\end{array}\right]$
How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?