Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-5+7*n)/(2+n)
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Limit of (-2+x)/(-4+x)
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Limit of (-16+x^2-6*x)/(-2+x+x^2)
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Limit of (2+x^2-5*x)/(5+x^2+3*x^3)
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Identical expressions
- four *sqrt(x^ two)
- 4 multiply by square root of (x squared )
- four multiply by square root of (x to the power of two)
- 4*√(x^2)
- 4*sqrt(x2)
- 4*sqrtx2
- 4*sqrt(x²)
- 4*sqrt(x to the power of 2)
- 4sqrt(x^2)
- 4sqrt(x2)
- 4sqrtx2
- 4sqrtx^2
Limit of the function 4*sqrt(x^2)
The solution
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lim \4*\/ x /
x->1+
$$\lim_{x \to 1^+}\left(4 \sqrt{x^{2}}\right)$$
Limit(4*sqrt(x^2), 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
One‐sided limits
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lim \4*\/ x /
x->1+
$$\lim_{x \to 1^+}\left(4 \sqrt{x^{2}}\right)$$
4
$$4$$
= 4.0
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lim \4*\/ x /
x->1-
$$\lim_{x \to 1^-}\left(4 \sqrt{x^{2}}\right)$$
4
$$4$$
= 4.0
= 4.0
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 1^-}\left(4 \sqrt{x^{2}}\right) = 4$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(4 \sqrt{x^{2}}\right) = 4$$
$$\lim_{x \to \infty}\left(4 \sqrt{x^{2}}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(4 \sqrt{x^{2}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(4 \sqrt{x^{2}}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to -\infty}\left(4 \sqrt{x^{2}}\right) = \infty$$
More at x→-oo
More at x→1 from the left
$$\lim_{x \to 1^+}\left(4 \sqrt{x^{2}}\right) = 4$$
$$\lim_{x \to \infty}\left(4 \sqrt{x^{2}}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(4 \sqrt{x^{2}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(4 \sqrt{x^{2}}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to -\infty}\left(4 \sqrt{x^{2}}\right) = \infty$$
More at x→-oo
The graph