following is some more common functions that are

Question

Following is some more common functions that are "nice enough".

• Polynomials are nice enough for all x's.
• If f ( x) = p ( x ) /q (x ) then f(x) will be nice enough provided p(x) and q(x) both are nice enough & if we don't get division by zero at the point we're evaluating at.
• cos ( x ) , sin ( x ) are nice enough for all x's
• sec ( x ) , tan ( x ) are nice enough provided x ≠ ........., - 5 ?/2 , - 3 ?/2 , ?/2 , 3 ?/2 , 5 ?/2 , ...... In other terms secant & tangent are nice enough everywhere cosine isn't zero. To illustrates why recall that these are both actually rational functions & that cosine is in the denominator of both then go back up & look at the second bullet above.
• csc ( x ) , cot ( x ) are nice enough provided x ≠ ......, -2 ? , - ? , 0, ? , 2 ? ,..... In other terms cosecant & cotangent are nice enough everywhere sine isn't zero
• is nice enough for all x if n is odd.
• if n is even then is nice enough for x ≥ 0. Here we need x ≥ 0 to ignore having to deal along with complex values.
• a ^x , e^x are nice enough for all x's
• log_b x, ln x are nice enough for x>0. Recall we can just plug positive numbers into logarithms & not zero or negative numbers.
• Any sum, difference or product of the functions will also be nice enough.
• Quotients will be nice enough provided we don't obatin division by zero upon evaluating the limit.

The last bullet is significant. It means that for any combination of these functions all we have to do is evaluate the function at the point in question, ensuring that none of the restrictions are violated. It means that now we can do a large number of limits.