Posted by Anonymous on .
find the indicated limits, if they exist.
1. lim (3x^3+x^2+1)/(x^3+1)
x> infinity
2. find the slope of the tangent line to the graph of the given function at any point:
f(x) = 2x +7
Could anyone please, please, please explain to me how to do these problems? It seems like sometimes I can do the problem and I think I know it but then I get another one wrong. I need to know what I'm messing up on.

CalculusLimits 
MathMate,
For a function composed of a rational function, the limit to infinity can be determined by the quotient of the leading terms of the numerator and denominator:
Lim 3x^3/x^3 x>∞
= Lim 3 x>∞
=3
The slope of the tangent to the (line) is the coefficient of x, namely 2.
In a general way, the tangent function is obtained by taking the derivative of the function, i.e. d(2x+7)/dx = 2.