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-cos(x)+5*x
Limit of the function/ -cos(x)+5*x

Limit of the function -cos(x)+5*x

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You have entered [src] 
 lim (-cos(x) + 5*x)
x->0+
lim⁡x→0+(5x−cos⁡(x))\lim_{x \to 0^+}\left(5 x - \cos{\left(x \right)}\right) 
Limit(-cos(x) + 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
02468-8-6-4-2-1010-100100
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(5x−cos⁡(x))=−1\lim_{x \to 0^-}\left(5 x - \cos{\left(x \right)}\right) = -1
More at x→0 from the left
lim⁡x→0+(5x−cos⁡(x))=−1\lim_{x \to 0^+}\left(5 x - \cos{\left(x \right)}\right) = -1
lim⁡x→∞(5x−cos⁡(x))=∞\lim_{x \to \infty}\left(5 x - \cos{\left(x \right)}\right) = \infty
More at x→oo
lim⁡x→1−(5x−cos⁡(x))=5−cos⁡(1)\lim_{x \to 1^-}\left(5 x - \cos{\left(x \right)}\right) = 5 - \cos{\left(1 \right)}
More at x→1 from the left
lim⁡x→1+(5x−cos⁡(x))=5−cos⁡(1)\lim_{x \to 1^+}\left(5 x - \cos{\left(x \right)}\right) = 5 - \cos{\left(1 \right)}
More at x→1 from the right
lim⁡x→−∞(5x−cos⁡(x))=−∞\lim_{x \to -\infty}\left(5 x - \cos{\left(x \right)}\right) = -\infty
More at x→-oo
Rapid solution [src] 
-1
−1-1
Expand and simplify
One‐sided limits [src] 
 lim (-cos(x) + 5*x)
x->0+
lim⁡x→0+(5x−cos⁡(x))\lim_{x \to 0^+}\left(5 x - \cos{\left(x \right)}\right) 
-1
−1-1 
= -1.0
 lim (-cos(x) + 5*x)
x->0-
lim⁡x→0−(5x−cos⁡(x))\lim_{x \to 0^-}\left(5 x - \cos{\left(x \right)}\right) 
-1
−1-1 
= -1.0
= -1.0
Numerical answer [src] 
-1.0
-1.0
The graph
Limit of the function -cos(x)+5*x
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