Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1-4*x)^(1/x)
-
Limit of (-1+2*x^2+5*x^3)/(3+2*x)
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Limit of (5+x-3*x^2)/(4-x+2*x^2)
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Limit of ((1+2*x)/(2+2*x))^x
- Integral of d{x}:
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1/(cos(x)+sin(x))
- Graphing y =:
- 1/(cos(x)+sin(x))
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Identical expressions
- one /(cos(x)+sin(x))
- 1 divide by ( co sinus of e of (x) plus sinus of (x))
- one divide by ( co sinus of e of (x) plus sinus of (x))
- 1/cosx+sinx
- 1 divide by (cos(x)+sin(x))
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Similar expressions
- 1/(cos(x)-sin(x))
- 1/(cosx+sinx)
Limit of the function 1/(cos(x)+sin(x))
The solution
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[src]
1
lim ---------------
3*pi cos(x) + sin(x)
x->----+
4
$$\lim_{x \to \frac{3 \pi}{4}^+} \frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)}}$$
Limit(1/(cos(x) + sin(x)), x, (3*pi)/4)
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]
1
lim ---------------
3*pi cos(x) + sin(x)
x->----+
4
$$\lim_{x \to \frac{3 \pi}{4}^+} \frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)}}$$
-oo
$$-\infty$$
= -106.773904434225
1
lim ---------------
3*pi cos(x) + sin(x)
x->-----
4
$$\lim_{x \to \frac{3 \pi}{4}^-} \frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)}}$$
oo
$$\infty$$
= 106.773904434222
= 106.773904434222
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \frac{3 \pi}{4}^-} \frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)}} = -\infty$$
More at x→(3*pi)/4 from the left
$$\lim_{x \to \frac{3 \pi}{4}^+} \frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)}} = -\infty$$
$$\lim_{x \to \infty} \frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)}} = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-} \frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)}} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)}} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)}} = \frac{1}{\cos{\left(1 \right)} + \sin{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)}} = \frac{1}{\cos{\left(1 \right)} + \sin{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)}} = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
More at x→(3*pi)/4 from the left
$$\lim_{x \to \frac{3 \pi}{4}^+} \frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)}} = -\infty$$
$$\lim_{x \to \infty} \frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)}} = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-} \frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)}} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)}} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)}} = \frac{1}{\cos{\left(1 \right)} + \sin{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)}} = \frac{1}{\cos{\left(1 \right)} + \sin{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)}} = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
The graph