Insight number 2: to evaluate the limit of a: 1. Rational function: you can factorize and cancel out what you can
2. Radicals (subtractions of square roots): multiply and divide by the
conjugate. For example:
√x² +1-x
x² + 1 - x²
x2 + 1 - x=
(V x2 +1+
+x)
Vx2 + 1 + x
Vx2 + 1 + x
1
VX2 + 1 + x
3. Trigonometric functions: try to connect your limit with important
trigonometric limits like limx-
= 1
If you are stuck with a trig limit, express all the trig functions in terms
of sine and cosine.
4. If you are composing continuous functions, you can pass the limit
inside the external function: limz-a f(g(x)) = f(limz-a 9(x))
sin (x)