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(-56+h^2)/h
Limit of the function/ (-56+h^2)/h

Limit of the function (-56+h^2)/h

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The solution

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     /       2\
     |-56 + h |
 lim |--------|
h->0+\   h    /
lim⁡h→0+(h2−56h)\lim_{h \to 0^+}\left(\frac{h^{2} - 56}{h}\right) 
Limit((-56 + h^2)/h, h, 0)
Detail solution
Let's take the limit
lim⁡h→0+(h2−56h)\lim_{h \to 0^+}\left(\frac{h^{2} - 56}{h}\right)
transform
lim⁡h→0+(h2−56h)\lim_{h \to 0^+}\left(\frac{h^{2} - 56}{h}\right)
=
lim⁡h→0+(h2−56h)\lim_{h \to 0^+}\left(\frac{h^{2} - 56}{h}\right)
=
lim⁡h→0+(h−56h)=\lim_{h \to 0^+}\left(h - \frac{56}{h}\right) = 
False

= -oo

The final answer:
lim⁡h→0+(h2−56h)=−∞\lim_{h \to 0^+}\left(\frac{h^{2} - 56}{h}\right) = -\infty
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
02468-8-6-4-2-1010-1000010000
Plot the graph
Other limits h→0, -oo, +oo, 1
lim⁡h→0−(h2−56h)=−∞\lim_{h \to 0^-}\left(\frac{h^{2} - 56}{h}\right) = -\infty
More at h→0 from the left
lim⁡h→0+(h2−56h)=−∞\lim_{h \to 0^+}\left(\frac{h^{2} - 56}{h}\right) = -\infty
lim⁡h→∞(h2−56h)=∞\lim_{h \to \infty}\left(\frac{h^{2} - 56}{h}\right) = \infty
More at h→oo
lim⁡h→1−(h2−56h)=−55\lim_{h \to 1^-}\left(\frac{h^{2} - 56}{h}\right) = -55
More at h→1 from the left
lim⁡h→1+(h2−56h)=−55\lim_{h \to 1^+}\left(\frac{h^{2} - 56}{h}\right) = -55
More at h→1 from the right
lim⁡h→−∞(h2−56h)=−∞\lim_{h \to -\infty}\left(\frac{h^{2} - 56}{h}\right) = -\infty
More at h→-oo
One‐sided limits [src] 
     /       2\
     |-56 + h |
 lim |--------|
h->0+\   h    /
lim⁡h→0+(h2−56h)\lim_{h \to 0^+}\left(\frac{h^{2} - 56}{h}\right) 
-oo
−∞-\infty 
= -8455.99337748344
     /       2\
     |-56 + h |
 lim |--------|
h->0-\   h    /
lim⁡h→0−(h2−56h)\lim_{h \to 0^-}\left(\frac{h^{2} - 56}{h}\right) 
oo
∞\infty 
= 8455.99337748344
= 8455.99337748344
Rapid solution [src] 
-oo
−∞-\infty
Expand and simplify
Numerical answer [src] 
-8455.99337748344
-8455.99337748344
The graph
Limit of the function (-56+h^2)/h
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