Evaluate the following limit: _ x 3 (1 x-3 -3 x^2-3x ) - Vidyadip

Question

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow3}\Big(\frac{1}{\text{x}-3}-\frac{3}{\text{x}^2-3\text{x}}\Big)$

✓

Answer

$\lim\limits_{\text{x}\rightarrow3}\Big(\frac{1}{\text{x}-3}-\frac{3}{\text{x}^2-3\text{x}}\Big)$$=\lim\limits_{\text{x}\rightarrow3}\Big(\frac{1}{\text{x}-3}-\frac{3}{\text{x}(\text{x}-3)}\Big)$
$=\lim\limits_{\text{x}\rightarrow3}\Big(\frac{\text{x}-3}{\text{x}(\text{x}-3)}\Big)$
$=\lim\limits_{\text{x}\rightarrow3}\Big(\frac{1}{\text{x}}\Big)$
$=\frac{1}{3}$

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

Explore more

More "2 Marks Questions" from Limits→Limits — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Show the following quadratic equation:
$x^2 + 4ix - 4 = 0$

Prove that: $\cos \left(\frac{3 \pi}{2}+x\right) \cos (2 \pi+x)\left[\cot \left(\frac{3 \pi}{2}-x\right)+\cot (2 \pi+x)\right]=1$

If $A =\{1,2,3\}, B =\{2,3,4\}$ and $C =\{3,4,5,6\}$ then find $(A \cap B)-C$.

Eight chairs are numbered $1$ to $8$. Two women and $3$ men wish to occupy one chair each. First the women choose the chairs from amongst the chairs $1$ to $4$ and then men select from the remaining chairs. Find the total number of possible arrangements.
$[$Hint: $2$ women occupy the chair$,$ from $1$ to $4$ in $^4P_2$ ways and $3$ men occupy the remaining chairs in $^6P_3$ ways.]

Find the derivative of $(x^3 - 27)$ from first principle.

Differentiate the following function with respect to $\text{x}$:$\text{x}^3\text{e}^\text{x}$

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{a}^\text{x}+\text{b}^\text{x}+\text{c}^\text{x}-3}{\text{x}}$

Differentiate the following function with respect to (x):$\text{x}^4-2\sin\text{x}+\cos\text{x}$

Line through the points $(-2, 6)$ and $(4, 8)$ is perpendicular to the line through the points $(8, 12)$ and $(x, 24).$ Find the value of $x.$

Evaluate $\mathop {\lim }\limits_{x \to 0} \frac{{ax + x\cos x}}{{b\sin x}}.$