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Limit of the function/ f*(h+x)-f*x

Limit of the function f*(h+x)-f*x

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You have entered [src] 
 lim (f*(h + x) - f*x)
h->0+
lim⁡h→0+(−fx+f(h+x))\lim_{h \to 0^+}\left(- f x + f \left(h + x\right)\right) 
Limit(f*(h + x) - f*x, h, 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
Rapid solution [src] 
0
00
Expand and simplify
One‐sided limits [src] 
 lim (f*(h + x) - f*x)
h->0+
lim⁡h→0+(−fx+f(h+x))\lim_{h \to 0^+}\left(- f x + f \left(h + x\right)\right) 
0
00 
 lim (f*(h + x) - f*x)
h->0-
lim⁡h→0−(−fx+f(h+x))\lim_{h \to 0^-}\left(- f x + f \left(h + x\right)\right) 
0
00 
0
Other limits h→0, -oo, +oo, 1
lim⁡h→0−(−fx+f(h+x))=0\lim_{h \to 0^-}\left(- f x + f \left(h + x\right)\right) = 0
More at h→0 from the left
lim⁡h→0+(−fx+f(h+x))=0\lim_{h \to 0^+}\left(- f x + f \left(h + x\right)\right) = 0
lim⁡h→∞(−fx+f(h+x))=∞sign⁡(f)\lim_{h \to \infty}\left(- f x + f \left(h + x\right)\right) = \infty \operatorname{sign}{\left(f \right)}
More at h→oo
lim⁡h→1−(−fx+f(h+x))=f\lim_{h \to 1^-}\left(- f x + f \left(h + x\right)\right) = f
More at h→1 from the left
lim⁡h→1+(−fx+f(h+x))=f\lim_{h \to 1^+}\left(- f x + f \left(h + x\right)\right) = f
More at h→1 from the right
lim⁡h→−∞(−fx+f(h+x))=−∞sign⁡(f)\lim_{h \to -\infty}\left(- f x + f \left(h + x\right)\right) = - \infty \operatorname{sign}{\left(f \right)}
More at h→-oo
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