![]() We also highlight the importance of understanding various methods, such as direct substitution, factoring, multiplying by conjugates, and using trig identities. So there really is no general method that will work in all cases. In this video we explore strategies for determining which technique to use when finding limits. It is only really practical to evaluate approximations to it using numerical methods. Since x approaches larger positive values (infinity) x x. ![]() Is the root of #x^5+4x+2 = 0#, which is not expressible in terms of elementary functions. Solution to Example 9: We first factor out 16 x 2 under the square root of the denominator and take out of the square root and rewrite the limit as. This defines #y# as a function - let's call it #g(x)# - of #x#, since #x^5+4x+2# is continuous and strictly monotonically increasing, so has a continuous monotonic inverse. However, note that functions are not necessarily defined as #f(x) =. Sometimes it helps to use some kind of radical conjugate. If #f(x)# is a polynomial function, then we can find limits for finite values by substitution: See Example.This is not always feasible, but there are some cases that work. Setting it up piecewise can also be useful.
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