Question

9. Evaluate: lim sin2x.
x->π/4
​

Answer 1

Answer:

sin 2(π/4) = sin (π/2) =1

Answer 2

∴ $\lim_{x \to \frac{\pi }{4} }$  sin(2x) = 1

Given:

f(x) = sin2x.

To Find:

$\lim_{x \to \frac{\pi }{4} }$  sin(2x).

Solution:

We will use the following concepts to solve this problem :

$\lim_{x \to a} f(x) = f(a)$

$\lim_{n \to a} c = c$, where c is some constant.

Now, the given function is f(x) = sin2x

At x = π/4, f(x) becomes

sin 2(π/4) = sin (π/2) = 1

Now as x tends to π/4, the limit of the given function tends to:

$\lim_{x \to \frac{\pi }{4} }$  sin(2x) =  sin (2×π/4) = sin(π/2) = 1.

∴ $\lim_{x \to \frac{\pi }{4} }$  sin(2x) = 1

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