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5^x-cos(x)
Limit of the function/ 5^x-cos(x)

Limit of the function 5^x-cos(x)

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     / x         \
 lim \5  - cos(x)/
x->0+
lim⁡x→0+(5x−cos⁡(x))\lim_{x \to 0^+}\left(5^{x} - \cos{\left(x \right)}\right) 
Limit(5^x - cos(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
02468-8-6-4-2-1010-1000000010000000
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(5x−cos⁡(x))=0\lim_{x \to 0^-}\left(5^{x} - \cos{\left(x \right)}\right) = 0
More at x→0 from the left
lim⁡x→0+(5x−cos⁡(x))=0\lim_{x \to 0^+}\left(5^{x} - \cos{\left(x \right)}\right) = 0
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))=⟨−1,1⟩\lim_{x \to -\infty}\left(5^{x} - \cos{\left(x \right)}\right) = \left\langle -1, 1\right\rangle
More at x→-oo
One‐sided limits [src] 
     / x         \
 lim \5  - cos(x)/
x->0+
lim⁡x→0+(5x−cos⁡(x))\lim_{x \to 0^+}\left(5^{x} - \cos{\left(x \right)}\right) 
0
00 
= 1.65419556163526e-32
     / x         \
 lim \5  - cos(x)/
x->0-
lim⁡x→0−(5x−cos⁡(x))\lim_{x \to 0^-}\left(5^{x} - \cos{\left(x \right)}\right) 
0
00 
= -1.65067828187599e-30
= -1.65067828187599e-30
Rapid solution [src] 
0
00
Expand and simplify
Numerical answer [src] 
1.65419556163526e-32
1.65419556163526e-32
The graph
Limit of the function 5^x-cos(x)
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