Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-exp(-x)+exp(x))/(exp(x)+exp(-x))
-
Limit of ((3+5*x)/(-2+4*x))^(1+3*x)
-
Limit of (3+3*x^3+5*x+5*x^2)/(-1+x^2)
-
Limit of (3-x^2+5*x)/(4*x^7+81*x)
-
Identical expressions
- (one /sin(x))^tan(x)
- (1 divide by sinus of (x)) to the power of tangent of (x)
- (one divide by sinus of (x)) to the power of tangent of (x)
- (1/sin(x))tan(x)
- 1/sinxtanx
- 1/sinx^tanx
- (1 divide by sin(x))^tan(x)
-
Similar expressions
- (1/sinx)^tan(x)
Limit of the function (1/sin(x))^tan(x)
The solution
You have entered
[src]
tan(x)
/ 1 \
lim |------|
x->0+\sin(x)/
$$\lim_{x \to 0^+} \left(\frac{1}{\sin{\left(x \right)}}\right)^{\tan{\left(x \right)}}$$
Limit((1/sin(x))^tan(x), x, 0)
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
One‐sided limits
[src]
tan(x)
/ 1 \
lim |------|
x->0+\sin(x)/
$$\lim_{x \to 0^+} \left(\frac{1}{\sin{\left(x \right)}}\right)^{\tan{\left(x \right)}}$$
1
$$1$$
= 1.00163490275634
tan(x)
/ 1 \
lim |------|
x->0-\sin(x)/
$$\lim_{x \to 0^-} \left(\frac{1}{\sin{\left(x \right)}}\right)^{\tan{\left(x \right)}}$$
1
$$1$$
= (0.998071492041113 - 0.000766527748721653j)
= (0.998071492041113 - 0.000766527748721653j)
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \left(\frac{1}{\sin{\left(x \right)}}\right)^{\tan{\left(x \right)}} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\frac{1}{\sin{\left(x \right)}}\right)^{\tan{\left(x \right)}} = 1$$
$$\lim_{x \to \infty} \left(\frac{1}{\sin{\left(x \right)}}\right)^{\tan{\left(x \right)}}$$
More at x→oo
$$\lim_{x \to 1^-} \left(\frac{1}{\sin{\left(x \right)}}\right)^{\tan{\left(x \right)}} = \sin^{- \tan{\left(1 \right)}}{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\frac{1}{\sin{\left(x \right)}}\right)^{\tan{\left(x \right)}} = \sin^{- \tan{\left(1 \right)}}{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(\frac{1}{\sin{\left(x \right)}}\right)^{\tan{\left(x \right)}}$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\frac{1}{\sin{\left(x \right)}}\right)^{\tan{\left(x \right)}} = 1$$
$$\lim_{x \to \infty} \left(\frac{1}{\sin{\left(x \right)}}\right)^{\tan{\left(x \right)}}$$
More at x→oo
$$\lim_{x \to 1^-} \left(\frac{1}{\sin{\left(x \right)}}\right)^{\tan{\left(x \right)}} = \sin^{- \tan{\left(1 \right)}}{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\frac{1}{\sin{\left(x \right)}}\right)^{\tan{\left(x \right)}} = \sin^{- \tan{\left(1 \right)}}{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(\frac{1}{\sin{\left(x \right)}}\right)^{\tan{\left(x \right)}}$$
More at x→-oo
The graph