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6+3*x/2
Limit of the function/ 6+3*x/2

Limit of the function 6+3*x/2

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     /    3*x\
 lim |6 + ---|
x->3+\     2 /
$$\lim_{x \to 3^+}\left(\frac{3 x}{2} + 6\right)$$ 
Limit(6 + (3*x)/2, x, 3)
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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One‐sided limits [src] 
     /    3*x\
 lim |6 + ---|
x->3+\     2 /
$$\lim_{x \to 3^+}\left(\frac{3 x}{2} + 6\right)$$ 
21/2
$$\frac{21}{2}$$ 
= 10.5
     /    3*x\
 lim |6 + ---|
x->3-\     2 /
$$\lim_{x \to 3^-}\left(\frac{3 x}{2} + 6\right)$$ 
21/2
$$\frac{21}{2}$$ 
= 10.5
= 10.5
Rapid solution [src] 
21/2
$$\frac{21}{2}$$
Expand and simplify
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 3^-}\left(\frac{3 x}{2} + 6\right) = \frac{21}{2}$$
More at x→3 from the left
$$\lim_{x \to 3^+}\left(\frac{3 x}{2} + 6\right) = \frac{21}{2}$$
$$\lim_{x \to \infty}\left(\frac{3 x}{2} + 6\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{3 x}{2} + 6\right) = 6$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{3 x}{2} + 6\right) = 6$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{3 x}{2} + 6\right) = \frac{15}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{3 x}{2} + 6\right) = \frac{15}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{3 x}{2} + 6\right) = -\infty$$
More at x→-oo
Numerical answer [src] 
10.5
10.5
The graph
Limit of the function 6+3*x/2
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