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(1-tan(x))^(x/7)
Limit of the function/ (1-tan(x))^(x/7)

Limit of the function (1-tan(x))^(x/7)

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                 x
                 -
                 7
 lim (1 - tan(x)) 
x->0+
lim⁡x→0+(1−tan⁡(x))x7\lim_{x \to 0^+} \left(1 - \tan{\left(x \right)}\right)^{\frac{x}{7}} 
Limit((1 - tan(x))^(x/7), 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
02468-8-6-4-2-1010020
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(1−tan⁡(x))x7=1\lim_{x \to 0^-} \left(1 - \tan{\left(x \right)}\right)^{\frac{x}{7}} = 1
More at x→0 from the left
lim⁡x→0+(1−tan⁡(x))x7=1\lim_{x \to 0^+} \left(1 - \tan{\left(x \right)}\right)^{\frac{x}{7}} = 1
lim⁡x→∞(1−tan⁡(x))x7\lim_{x \to \infty} \left(1 - \tan{\left(x \right)}\right)^{\frac{x}{7}}
More at x→oo
lim⁡x→1−(1−tan⁡(x))x7=−17−1+tan⁡(1)7\lim_{x \to 1^-} \left(1 - \tan{\left(x \right)}\right)^{\frac{x}{7}} = \sqrt[7]{-1} \sqrt[7]{-1 + \tan{\left(1 \right)}}
More at x→1 from the left
lim⁡x→1+(1−tan⁡(x))x7=−17−1+tan⁡(1)7\lim_{x \to 1^+} \left(1 - \tan{\left(x \right)}\right)^{\frac{x}{7}} = \sqrt[7]{-1} \sqrt[7]{-1 + \tan{\left(1 \right)}}
More at x→1 from the right
lim⁡x→−∞(1−tan⁡(x))x7\lim_{x \to -\infty} \left(1 - \tan{\left(x \right)}\right)^{\frac{x}{7}}
More at x→-oo
Rapid solution [src] 
1
11
Expand and simplify
One‐sided limits [src] 
                 x
                 -
                 7
 lim (1 - tan(x)) 
x->0+
lim⁡x→0+(1−tan⁡(x))x7\lim_{x \to 0^+} \left(1 - \tan{\left(x \right)}\right)^{\frac{x}{7}} 
1
11 
= 1.0
                 x
                 -
                 7
 lim (1 - tan(x)) 
x->0-
lim⁡x→0−(1−tan⁡(x))x7\lim_{x \to 0^-} \left(1 - \tan{\left(x \right)}\right)^{\frac{x}{7}} 
1
11 
= 1.0
= 1.0
Numerical answer [src] 
1.0
1.0
The graph
Limit of the function (1-tan(x))^(x/7)
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