diff --git a/diofant/core/expr.py b/diofant/core/expr.py
index 5871995aa4f..3b3aa3d9113 100644
--- a/diofant/core/expr.py
+++ b/diofant/core/expr.py
@@ -485,7 +485,7 @@ def is_constant(self, *wrt, **flags):
                     if a is None or a is nan:
                         # try random real
                         a = expr._random(None, -1, 0, 1, 0)
-            except ZeroDivisionError:
+            except (ZeroDivisionError, TypeError):
                 a = None
             if a is not None and a is not nan:
                 try:
@@ -494,7 +494,7 @@ def is_constant(self, *wrt, **flags):
                     if b is nan:
                         # evaluation may succeed when substitution fails
                         b = expr._random(None, 1, 0, 1, 0)
-                except ZeroDivisionError:
+                except (ZeroDivisionError, TypeError):
                     b = None
                 if b is not None and b is not nan and b.equals(a) is False:
                     return False
diff --git a/diofant/series/gruntz.py b/diofant/series/gruntz.py
index f5d6b2782e3..d9ca5033832 100644
--- a/diofant/series/gruntz.py
+++ b/diofant/series/gruntz.py
@@ -134,6 +134,14 @@ def mrv(e, x):
         return mrv(e.base, x)
     elif isinstance(e, log):
         return mrv(e.args[0], x)
+    elif e.is_Piecewise:
+        for a, c in e.args:
+            if not c.is_Atom:
+                c = c.func(c.lhs - c.rhs)
+                c = c.func(limitinf(c.lhs, x))
+                if c:
+                    break
+        return mrv(a, x)
     elif e.is_Function and not isinstance(e.func, UndefinedFunction):
         return functools.reduce(lambda a, b: mrv_max(a, b, x),
                                 [mrv(a, x) for a in e.args])
diff --git a/diofant/tests/series/test_limits.py b/diofant/tests/series/test_limits.py
index e775d2f6f4c..577372fa6bb 100644
--- a/diofant/tests/series/test_limits.py
+++ b/diofant/tests/series/test_limits.py
@@ -99,6 +99,17 @@ def test_basic4():
     e = ((n**(n + 1) + (n + 1)**n)/n**(n + 1))**n
     assert limit(e, n, oo) == E**E
 
+    # issue sympy/sympy#18492
+    e1 = 2*sqrt(x)*Piecewise(((4*x - 2)/abs(sqrt(4 - 4*(2*x - 1)**2)),
+                              4*x - 2 >= 0),
+                             ((2 - 4*x)/abs(sqrt(4 - 4*(2*x - 1)**2)), True))
+    e2 = Piecewise((x**2/2, x <= Rational(1, 2)), (x/2 - Rational(1, 8), True))
+    e3 = Piecewise(((x - 9)/5, x < -1), ((x - 9)/5, x > 4),
+                   (sqrt(abs(x - 3)), True))
+    assert limit(e1, x, 0) == 1
+    assert limit(e2, x, 0) == 0
+    assert limit(e3, x, -1) == 2
+
 
 def test_basic5():
     class MyFunction(Function):
diff --git a/docs/release/notes-0.14.rst b/docs/release/notes-0.14.rst
index 16a3e887073..5cee93a6039 100644
--- a/docs/release/notes-0.14.rst
+++ b/docs/release/notes-0.14.rst
@@ -24,6 +24,7 @@ Minor changes
 =============
 
 * Support unevaluated :class:`~diofant.polys.rootoftools.RootOf`'s over finite fields, see :pull:`1209`.
+* Support calculating limits with :class:`~diofant.functions.elementary.piecewise.Piecewise` functions, see :pull:`1214`.
 
 Developer changes
 =================
@@ -65,3 +66,4 @@ These Sympy issues also were addressed:
 * :sympyissue:`23231`: Sympy giving the wrong solution
 * :sympyissue:`14387`: Tutorial on limits creates impression that they are two-sided by default
 * :sympyissue:`8166`: Limit assumes function is continuous?
+* :sympyissue:`18492`: Limit of Piecewise function - NotImplementedError: Don't know how to calculate the mrv