limit x->1- tan(arcsin(x)) — step-by-step solution

Let's evaluate the limit of

\tan (\arcsin (x))

when

x \to 1

⁻

ⓘ The function arcsin is continuous, its limit is its value at the limit of its argument

The limit of

\arcsin (x)

\arcsin (1)

⁻ when

x \to 1

⁻

⇥Let's calculate:

\arcsin (1)

⇥ⓘ acos, asin and atan give the angle whose cosine, sine or tangent is the number, here a remarkable value:

\arcsin (1)

\frac{π}{2}

⇥

\frac{π}{2}

ⓘ This is a reference limit of the function tan

So the limit of

\tan (\arcsin (x))

+∞

when

x \to 1

⁻

▶Limit:

+∞