Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1+5*x+9*x^2)/(-2-7*x+2*x^3+4*x^2)
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Limit of (-1+7*x^2)/(1-2*x+4*x^2+5*x^3)
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Limit of 7*x^2/(-1+e^(3*x))
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Limit of (-2*n^2+4*n+7*n^3)/(5+2*n^3)
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Identical expressions
- (one +sin(four *x))^(one /x)
- (1 plus sinus of (4 multiply by x)) to the power of (1 divide by x)
- (one plus sinus of (four multiply by x)) to the power of (one divide by x)
- (1+sin(4*x))(1/x)
- 1+sin4*x1/x
- (1+sin(4x))^(1/x)
- (1+sin(4x))(1/x)
- 1+sin4x1/x
- 1+sin4x^1/x
- (1+sin(4*x))^(1 divide by x)
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Similar expressions
- (1-sin(4*x))^(1/x)
Limit of the function (1+sin(4*x))^(1/x)
The solution
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[src]
x ______________ lim \/ 1 + sin(4*x) x->0+
$$\lim_{x \to 0^+} \left(\sin{\left(4 x \right)} + 1\right)^{1 \cdot \frac{1}{x}}$$
Limit((1 + sin(4*x))^(1/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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \left(\sin{\left(4 x \right)} + 1\right)^{1 \cdot \frac{1}{x}} = e^{4}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\sin{\left(4 x \right)} + 1\right)^{1 \cdot \frac{1}{x}} = e^{4}$$
$$\lim_{x \to \infty} \left(\sin{\left(4 x \right)} + 1\right)^{1 \cdot \frac{1}{x}} = \left\langle 0, 1\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-} \left(\sin{\left(4 x \right)} + 1\right)^{1 \cdot \frac{1}{x}} = \sin{\left(4 \right)} + 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\sin{\left(4 x \right)} + 1\right)^{1 \cdot \frac{1}{x}} = \sin{\left(4 \right)} + 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(\sin{\left(4 x \right)} + 1\right)^{1 \cdot \frac{1}{x}} = \left\langle 1, \infty\right\rangle$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\sin{\left(4 x \right)} + 1\right)^{1 \cdot \frac{1}{x}} = e^{4}$$
$$\lim_{x \to \infty} \left(\sin{\left(4 x \right)} + 1\right)^{1 \cdot \frac{1}{x}} = \left\langle 0, 1\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-} \left(\sin{\left(4 x \right)} + 1\right)^{1 \cdot \frac{1}{x}} = \sin{\left(4 \right)} + 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\sin{\left(4 x \right)} + 1\right)^{1 \cdot \frac{1}{x}} = \sin{\left(4 \right)} + 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(\sin{\left(4 x \right)} + 1\right)^{1 \cdot \frac{1}{x}} = \left\langle 1, \infty\right\rangle$$
More at x→-oo
One‐sided limits
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x ______________ lim \/ 1 + sin(4*x) x->0+
$$\lim_{x \to 0^+} \left(\sin{\left(4 x \right)} + 1\right)^{1 \cdot \frac{1}{x}}$$
4 e
$$e^{4}$$
= 54.5981500331442
x ______________ lim \/ 1 + sin(4*x) x->0-
$$\lim_{x \to 0^-} \left(\sin{\left(4 x \right)} + 1\right)^{1 \cdot \frac{1}{x}}$$
4 e
$$e^{4}$$
= 54.5981500331442
= 54.5981500331442
The graph