Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (2+x^2+3*x)/(2+2*x^2+5*x)
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Limit of (-51+x^2-14*x)/(-21+x^2-4*x)
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Limit of (-1+x)/(3-2*x)
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Limit of -sec(x)+tan(x)
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Identical expressions
- (- one + three *sqrt(x)+ eight *x^ two)/(x+sin(five *x))
- ( minus 1 plus 3 multiply by square root of (x) plus 8 multiply by x squared ) divide by (x plus sinus of (5 multiply by x))
- ( minus one plus three multiply by square root of (x) plus eight multiply by x to the power of two) divide by (x plus sinus of (five multiply by x))
- (-1+3*√(x)+8*x^2)/(x+sin(5*x))
- (-1+3*sqrt(x)+8*x2)/(x+sin(5*x))
- -1+3*sqrtx+8*x2/x+sin5*x
- (-1+3*sqrt(x)+8*x²)/(x+sin(5*x))
- (-1+3*sqrt(x)+8*x to the power of 2)/(x+sin(5*x))
- (-1+3sqrt(x)+8x^2)/(x+sin(5x))
- (-1+3sqrt(x)+8x2)/(x+sin(5x))
- -1+3sqrtx+8x2/x+sin5x
- -1+3sqrtx+8x^2/x+sin5x
- (-1+3*sqrt(x)+8*x^2) divide by (x+sin(5*x))
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Similar expressions
- (-1+3*sqrt(x)-8*x^2)/(x+sin(5*x))
- (-1+3*sqrt(x)+8*x^2)/(x-sin(5*x))
- (-1-3*sqrt(x)+8*x^2)/(x+sin(5*x))
- (1+3*sqrt(x)+8*x^2)/(x+sin(5*x))
Limit of the function (-1+3*sqrt(x)+8*x^2)/(x+sin(5*x))
The solution
You have entered
[src]
/ ___ 2\
|-1 + 3*\/ x + 8*x |
lim |-------------------|
x->0+\ x + sin(5*x) /
$$\lim_{x \to 0^+}\left(\frac{8 x^{2} + \left(3 \sqrt{x} - 1\right)}{x + \sin{\left(5 x \right)}}\right)$$
Limit((-1 + 3*sqrt(x) + 8*x^2)/(x + sin(5*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]
/ ___ 2\
|-1 + 3*\/ x + 8*x |
lim |-------------------|
x->0+\ x + sin(5*x) /
$$\lim_{x \to 0^+}\left(\frac{8 x^{2} + \left(3 \sqrt{x} - 1\right)}{x + \sin{\left(5 x \right)}}\right)$$
-oo
$$-\infty$$
= -19.016629546138
/ ___ 2\
|-1 + 3*\/ x + 8*x |
lim |-------------------|
x->0-\ x + sin(5*x) /
$$\lim_{x \to 0^-}\left(\frac{8 x^{2} + \left(3 \sqrt{x} - 1\right)}{x + \sin{\left(5 x \right)}}\right)$$
oo
$$\infty$$
= (25.1616681482 - 6.14503860206197j)
= (25.1616681482 - 6.14503860206197j)
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{8 x^{2} + \left(3 \sqrt{x} - 1\right)}{x + \sin{\left(5 x \right)}}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{8 x^{2} + \left(3 \sqrt{x} - 1\right)}{x + \sin{\left(5 x \right)}}\right) = -\infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{8 x^{2} + \left(3 \sqrt{x} - 1\right)}{x + \sin{\left(5 x \right)}}\right) = \frac{10}{\sin{\left(5 \right)} + 1}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{8 x^{2} + \left(3 \sqrt{x} - 1\right)}{x + \sin{\left(5 x \right)}}\right) = \frac{10}{\sin{\left(5 \right)} + 1}$$
More at x→1 from the right
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{8 x^{2} + \left(3 \sqrt{x} - 1\right)}{x + \sin{\left(5 x \right)}}\right) = -\infty$$
False
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{8 x^{2} + \left(3 \sqrt{x} - 1\right)}{x + \sin{\left(5 x \right)}}\right) = \frac{10}{\sin{\left(5 \right)} + 1}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{8 x^{2} + \left(3 \sqrt{x} - 1\right)}{x + \sin{\left(5 x \right)}}\right) = \frac{10}{\sin{\left(5 \right)} + 1}$$
More at x→1 from the right
False
More at x→-oo
The graph