Mister Exam
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- 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 -sec(x)+tan(x)
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Limit of tan(3*x)/(4*x)
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Identical expressions
- -sec(x)+tan(x)
- minus sec(x) plus tangent of (x)
- -secx+tanx
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Similar expressions
- -sec(x)-tan(x)
- sec(x)+tan(x)
Limit of the function -sec(x)+tan(x)
The solution
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lim (-sec(x) + tan(x)) pi x->--+ 2
$$\lim_{x \to \frac{\pi}{2}^+}\left(\tan{\left(x \right)} - \sec{\left(x \right)}\right)$$
Limit(-sec(x) + tan(x), x, pi/2)
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 (-sec(x) + tan(x)) pi x->--+ 2
$$\lim_{x \to \frac{\pi}{2}^+}\left(\tan{\left(x \right)} - \sec{\left(x \right)}\right)$$
0
$$0$$
= -3.06161699786838e-17
lim (-sec(x) + tan(x)) pi x->--- 2
$$\lim_{x \to \frac{\pi}{2}^-}\left(\tan{\left(x \right)} - \sec{\left(x \right)}\right)$$
0
$$0$$
= -3.06161699786839e-17
= -3.06161699786839e-17
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \frac{\pi}{2}^-}\left(\tan{\left(x \right)} - \sec{\left(x \right)}\right) = 0$$
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+}\left(\tan{\left(x \right)} - \sec{\left(x \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(\tan{\left(x \right)} - \sec{\left(x \right)}\right)$$
More at x→oo
$$\lim_{x \to 0^-}\left(\tan{\left(x \right)} - \sec{\left(x \right)}\right) = -1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\tan{\left(x \right)} - \sec{\left(x \right)}\right) = -1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\tan{\left(x \right)} - \sec{\left(x \right)}\right) = \frac{-1 + \cos{\left(1 \right)} \tan{\left(1 \right)}}{\cos{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\tan{\left(x \right)} - \sec{\left(x \right)}\right) = \frac{-1 + \cos{\left(1 \right)} \tan{\left(1 \right)}}{\cos{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\tan{\left(x \right)} - \sec{\left(x \right)}\right)$$
More at x→-oo
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+}\left(\tan{\left(x \right)} - \sec{\left(x \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(\tan{\left(x \right)} - \sec{\left(x \right)}\right)$$
More at x→oo
$$\lim_{x \to 0^-}\left(\tan{\left(x \right)} - \sec{\left(x \right)}\right) = -1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\tan{\left(x \right)} - \sec{\left(x \right)}\right) = -1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\tan{\left(x \right)} - \sec{\left(x \right)}\right) = \frac{-1 + \cos{\left(1 \right)} \tan{\left(1 \right)}}{\cos{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\tan{\left(x \right)} - \sec{\left(x \right)}\right) = \frac{-1 + \cos{\left(1 \right)} \tan{\left(1 \right)}}{\cos{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\tan{\left(x \right)} - \sec{\left(x \right)}\right)$$
More at x→-oo
The graph