Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (2^(1+2*x)+3^(2+x))/(5+4^(2+x))
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Limit of 1/(x*(3+x))
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Limit of 1+x*log(2+x)
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Limit of ((1+x^2)^(1/3)-x*cot(x))/(x*sin(x))
- Integral of d{x}:
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1+x^4
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Identical expressions
- one +x^ four
- 1 plus x to the power of 4
- one plus x to the power of four
- 1+x4
- 1+x⁴
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Similar expressions
- 1-x^4
- (-5*x^2+3*sqrt(2+x^2))/(x-sqrt(1+x^4-x))
- (1+x^4)/(-2+x^2+3*x)
- (1+x^8-2*x)/(1+x^4-2*x)
Limit of the function 1+x^4
The solution
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[src]
/ 4\ lim \1 + x / x->0+
$$\lim_{x \to 0^+}\left(x^{4} + 1\right)$$
Limit(1 + x^4, 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
$$\lim_{x \to 0^-}\left(x^{4} + 1\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{4} + 1\right) = 1$$
$$\lim_{x \to \infty}\left(x^{4} + 1\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(x^{4} + 1\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{4} + 1\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{4} + 1\right) = \infty$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{4} + 1\right) = 1$$
$$\lim_{x \to \infty}\left(x^{4} + 1\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(x^{4} + 1\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{4} + 1\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{4} + 1\right) = \infty$$
More at x→-oo
One‐sided limits
[src]
/ 4\ lim \1 + x / x->0+
$$\lim_{x \to 0^+}\left(x^{4} + 1\right)$$
1
$$1$$
= 1
/ 4\ lim \1 + x / x->0-
$$\lim_{x \to 0^-}\left(x^{4} + 1\right)$$
1
$$1$$
= 1
= 1
The graph