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Limit of the function (5+3*x)/(-5+x)

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     /5 + 3*x\
 lim |-------|
x->7+\ -5 + x/

\lim_{x \to 7^+}\left(\frac{3 x + 5}{x - 5}\right)

Limit((5 + 3*x)/(-5 + x), x, 7)

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

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Other limits x→0, -oo, +oo, 1

\lim_{x \to 7^-}\left(\frac{3 x + 5}{x - 5}\right) = 13

\lim_{x \to 7^+}\left(\frac{3 x + 5}{x - 5}\right) = 13

\lim_{x \to \infty}\left(\frac{3 x + 5}{x - 5}\right) = 3

\lim_{x \to 0^-}\left(\frac{3 x + 5}{x - 5}\right) = -1

\lim_{x \to 0^+}\left(\frac{3 x + 5}{x - 5}\right) = -1

\lim_{x \to 1^-}\left(\frac{3 x + 5}{x - 5}\right) = -2

\lim_{x \to 1^+}\left(\frac{3 x + 5}{x - 5}\right) = -2

\lim_{x \to -\infty}\left(\frac{3 x + 5}{x - 5}\right) = 3

One‐sided limits [src]

     /5 + 3*x\
 lim |-------|
x->7+\ -5 + x/

\lim_{x \to 7^+}\left(\frac{3 x + 5}{x - 5}\right)

13

= 13.0

     /5 + 3*x\
 lim |-------|
x->7-\ -5 + x/

\lim_{x \to 7^-}\left(\frac{3 x + 5}{x - 5}\right)

13

= 13.0

= 13.0

Rapid solution [src]

13

Expand and simplify

Numerical answer [src]

13.0

13.0

The graph