Evaluate the following limit: _ x 0 ax+x b - Vidyadip

Question

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{ax}+\text{x}\cos\text{x}}{\text{b}\sin\text{x}}$

✓

Answer

$\lim\limits_{\text{x}\rightarrow0}\frac{\text{ax}+\text{x}\cos\text{x}}{\text{b}\sin\text{x}}$
$=\lim\limits_{\text{x}\rightarrow0}\frac{\text{a}+\cos\text{x}}{\frac{\text{b}\sin\text{x}}{\text{x}}}$
$=\frac{\lim\limits_{\text{x} \rightarrow0}\text{a}+\lim\limits_{\text{x} \rightarrow0}\cos\text{x}}{\lim\limits_{\text{x}\rightarrow0}\frac{\text{b}\sin\text{x}}{\text{x}}}$
$=\frac{\text{a}+1}{\text{b}}$ $\Big[\because\lim\limits_{\theta\rightarrow0}\frac{\sin\theta}{\theta}=1\Big]$
$=\frac{\text{a}+1}{\text{b}}$

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 "3 Marks Question" 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

Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5.

Differentiate the following functions with respect to x:$\frac{\text{x}^2-\text{x}+1}{\text{x}^2+\text{x}+1}$

Check the validity of the statements given below by the method given against it.
q: If n is a real number with $n > 3$, then $n2 > 9$ (by contradiction method).

In what ratio is the line joining A (-1, 1) and B(5, 7) divided by the line x + y = 4?

If $\tan\text{A}=\frac{\text{m}}{\text{m-1}}$ and $\tan\text{B}=\frac{1}{\text{2m-1}},$ then prove that $\text{A-B}=\frac{\pi}{4}$

Find the domain and range of the function $f(x)=\frac{x^2-9}{x-3}$

Differentiate the following function with respect to x:$\text{x}^5(3-\text{6x}^{-9})$

Solve the following system of equations in R.
$\frac{|\text{x}+2|-\text{x}}{\text{x}}<2$

Ravi obtained 70 and 75 marks in first two unit tests. Find the minimum marks he should get in the third test to have an average of at least 60 marks.

Solve the following equations: $\sin\theta+\sin5\theta=\sin3\theta$