Question

Plz. Solve Ques-11

I'll mark the correct answer as brainiest.

Correct answer= 3

Answer 1

Answer:3

Step-by-step explanation:

I'll try to explain each step.

1. A function is continuos when it's limit at a certain point is equal to the function value at that point. So, for this function to be continuous, its limit as x approaches 0 should be 1.

So, $\lim_{x \to \0} \frac{tan 3x}{kx}$ should be 1.

2. We know the limit of tan(x)/x as x tends to zero (it's 1)

3. Now we have tan (3x) in numerator and kx in denominator.

4. Take 3x as y. Also as x approaches 0, y also approaches zero. Since, y = 3x

x = y/3.

5. Rewriting the limit expression with y:

$\lim_{y \to \0} \frac{tan y}{k * y/3} =$  $3/k * \lim_{x \to \0} \frac{tan y}{y}$

6. Now, clearly for this limit to be equal to 1, k = 3.