Problem 3
Given \(q=5-1 / v,(v \neq 0),\) find: (a) \(\lim _{x \rightarrow+\infty} 9\) (b) \(\lim _{n \rightarrow-\infty} 9\)
Problem 3
Given the function \(y=5 x-2\) (a) find the difference quotient \(\Delta y / \Delta x\). What type of function is it? (b) since the expression \(\Delta x\) does not appear in the function \(\Delta y / \Delta x\) in part \((a),\) does it make any difference to the value of \(\Delta y / \Delta x\) whether \(\Delta x\) is large or small? Consequently, what is the limit of the difference quotient as \(\Delta x\) approaches zero?
Problem 3
Find the limits of \(q=(3 v+5) /(v+2)\) \((a)\) As \(v \rightarrow 0\) (b) As \(v \rightarrow 5\) (c) As \(v \rightarrow-1\)
Problem 4
Given \(y=f(x)=\frac{x^{2}-9 x+20}{x-4}\) (a) Is it possible to apply the quotient limit theorem to find the limit of this function as \(x \rightarrow 4 ?\) (b) is this function continuous at \(x=4 ?\) Why? (c) Find a function which, for \(x \neq 4,\) is equivalent to the given function, and obtain from the equivalent function the limit of \(y\) as \(x \rightarrow 4\)
