Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of 10+x^2+3*x^3+8*x
-
Limit of (-2+sqrt(x))/(-4+x^2)
-
Limit of x+2*x^3+5*x^4-x^2/3
-
Limit of (-x^3+2*x+5*x^4)/(1+x^4-8*x^3)
-
Identical expressions
- cos(four *x)^cot(x)
- co sinus of e of (4 multiply by x) to the power of cotangent of (x)
- co sinus of e of (four multiply by x) to the power of cotangent of (x)
- cos(4*x)cot(x)
- cos4*xcotx
- cos(4x)^cot(x)
- cos(4x)cot(x)
- cos4xcotx
- cos4x^cotx
Limit of the function cos(4*x)^cot(x)
The solution
You have entered
[src]
cot(x) lim cos (4*x) x->0+
$$\lim_{x \to 0^+} \cos^{\cot{\left(x \right)}}{\left(4 x \right)}$$
Limit(cos(4*x)^cot(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]
cot(x) lim cos (4*x) x->0+
$$\lim_{x \to 0^+} \cos^{\cot{\left(x \right)}}{\left(4 x \right)}$$
1
$$1$$
= 1.0
cot(x) lim cos (4*x) x->0-
$$\lim_{x \to 0^-} \cos^{\cot{\left(x \right)}}{\left(4 x \right)}$$
1
$$1$$
= 1.0
= 1.0
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \cos^{\cot{\left(x \right)}}{\left(4 x \right)} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos^{\cot{\left(x \right)}}{\left(4 x \right)} = 1$$
$$\lim_{x \to \infty} \cos^{\cot{\left(x \right)}}{\left(4 x \right)}$$
More at x→oo
$$\lim_{x \to 1^-} \cos^{\cot{\left(x \right)}}{\left(4 x \right)} = \left(- \cos{\left(4 \right)}\right)^{\frac{1}{\tan{\left(1 \right)}}} e^{\frac{i \pi}{\tan{\left(1 \right)}}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos^{\cot{\left(x \right)}}{\left(4 x \right)} = \left(- \cos{\left(4 \right)}\right)^{\frac{1}{\tan{\left(1 \right)}}} e^{\frac{i \pi}{\tan{\left(1 \right)}}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos^{\cot{\left(x \right)}}{\left(4 x \right)}$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \cos^{\cot{\left(x \right)}}{\left(4 x \right)} = 1$$
$$\lim_{x \to \infty} \cos^{\cot{\left(x \right)}}{\left(4 x \right)}$$
More at x→oo
$$\lim_{x \to 1^-} \cos^{\cot{\left(x \right)}}{\left(4 x \right)} = \left(- \cos{\left(4 \right)}\right)^{\frac{1}{\tan{\left(1 \right)}}} e^{\frac{i \pi}{\tan{\left(1 \right)}}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos^{\cot{\left(x \right)}}{\left(4 x \right)} = \left(- \cos{\left(4 \right)}\right)^{\frac{1}{\tan{\left(1 \right)}}} e^{\frac{i \pi}{\tan{\left(1 \right)}}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos^{\cot{\left(x \right)}}{\left(4 x \right)}$$
More at x→-oo
The graph