Mister Exam

Other calculators:

(1+sin(x))^cot(x)
Limit of the function/ (1+sin(x))^cot(x)

Limit of the function (1+sin(x))^cot(x)

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
                 cot(x)
 lim (1 + sin(x))      
x->1+
lim⁡x→1+(sin⁡(x)+1)cot⁡(x)\lim_{x \to 1^+} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}} 
Limit((1 + sin(x))^cot(x), x, 1)
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
-2.0-1.5-1.0-0.52.00.00.51.01.505
Plot the graph
Rapid solution [src] 
              1   
            ------
            tan(1)
(1 + sin(1))
(sin⁡(1)+1)1tan⁡(1)\left(\sin{\left(1 \right)} + 1\right)^{\frac{1}{\tan{\left(1 \right)}}}
Expand and simplify
One‐sided limits [src] 
                 cot(x)
 lim (1 + sin(x))      
x->1+
lim⁡x→1+(sin⁡(x)+1)cot⁡(x)\lim_{x \to 1^+} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}} 
              1   
            ------
            tan(1)
(1 + sin(1))
(sin⁡(1)+1)1tan⁡(1)\left(\sin{\left(1 \right)} + 1\right)^{\frac{1}{\tan{\left(1 \right)}}} 
= 1.47999555699277
                 cot(x)
 lim (1 + sin(x))      
x->1-
lim⁡x→1−(sin⁡(x)+1)cot⁡(x)\lim_{x \to 1^-} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}} 
              1   
            ------
            tan(1)
(1 + sin(1))
(sin⁡(1)+1)1tan⁡(1)\left(\sin{\left(1 \right)} + 1\right)^{\frac{1}{\tan{\left(1 \right)}}} 
= 1.47999555699277
= 1.47999555699277
Other limits x→0, -oo, +oo, 1
lim⁡x→1−(sin⁡(x)+1)cot⁡(x)=(sin⁡(1)+1)1tan⁡(1)\lim_{x \to 1^-} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}} = \left(\sin{\left(1 \right)} + 1\right)^{\frac{1}{\tan{\left(1 \right)}}}
More at x→1 from the left
lim⁡x→1+(sin⁡(x)+1)cot⁡(x)=(sin⁡(1)+1)1tan⁡(1)\lim_{x \to 1^+} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}} = \left(\sin{\left(1 \right)} + 1\right)^{\frac{1}{\tan{\left(1 \right)}}}
lim⁡x→∞(sin⁡(x)+1)cot⁡(x)\lim_{x \to \infty} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}}
More at x→oo
lim⁡x→0−(sin⁡(x)+1)cot⁡(x)=e\lim_{x \to 0^-} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}} = e
More at x→0 from the left
lim⁡x→0+(sin⁡(x)+1)cot⁡(x)=e\lim_{x \to 0^+} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}} = e
More at x→0 from the right
lim⁡x→−∞(sin⁡(x)+1)cot⁡(x)\lim_{x \to -\infty} \left(\sin{\left(x \right)} + 1\right)^{\cot{\left(x \right)}}
More at x→-oo
Numerical answer [src] 
1.47999555699277
1.47999555699277
The graph
Limit of the function (1+sin(x))^cot(x)
    © Mister Exam – Calculator