Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-2*sin(2*x)+sin(4*x))/(x*log(cos(6*x)))
- Limit of i*n*(1+x)/x
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Limit of (e^(2*x))^(1/log(1-2*x^2))
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Limit of (-1-x+5*x^2)/(2+3*x^2)
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Identical expressions
- i*n*(one +x)/x
- i multiply by n multiply by (1 plus x) divide by x
- i multiply by n multiply by (one plus x) divide by x
- in(1+x)/x
- in1+x/x
- i*n*(1+x) divide by x
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Similar expressions
- i*n*(1-x)/x
- sin((1+x)/x)
Limit of the function i*n*(1+x)/x
The solution
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[src]
/I*n*(1 + x)\ lim |-----------| x->0+\ x /
$$\lim_{x \to 0^+}\left(\frac{i n \left(x + 1\right)}{x}\right)$$
Limit(((i*n)*(1 + x))/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
One‐sided limits
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/I*n*(1 + x)\ lim |-----------| x->0+\ x /
$$\lim_{x \to 0^+}\left(\frac{i n \left(x + 1\right)}{x}\right)$$
oo*I*n
$$\infty i n$$
/I*n*(1 + x)\ lim |-----------| x->0-\ x /
$$\lim_{x \to 0^-}\left(\frac{i n \left(x + 1\right)}{x}\right)$$
-oo*I*n
$$- \infty i n$$
-oo*i*n
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{i n \left(x + 1\right)}{x}\right) = \infty i n$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{i n \left(x + 1\right)}{x}\right) = \infty i n$$
$$\lim_{x \to \infty}\left(\frac{i n \left(x + 1\right)}{x}\right) = i n$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{i n \left(x + 1\right)}{x}\right) = 2 i n$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{i n \left(x + 1\right)}{x}\right) = 2 i n$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{i n \left(x + 1\right)}{x}\right) = i n$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{i n \left(x + 1\right)}{x}\right) = \infty i n$$
$$\lim_{x \to \infty}\left(\frac{i n \left(x + 1\right)}{x}\right) = i n$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{i n \left(x + 1\right)}{x}\right) = 2 i n$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{i n \left(x + 1\right)}{x}\right) = 2 i n$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{i n \left(x + 1\right)}{x}\right) = i n$$
More at x→-oo