\(lim_{x\rightarrow\infty}{sin \ x \over x} \)

\(lim_{x\rightarrow {\pi/2}}{2x-\pi\over cosx} \)

\(lim_{x \rightarrow \infty}{\sqrt{x^2-1}\over 2x+1}=\)

If f(x) = x(-1)^{\(\left\lfloor 1\over x \right\rfloor \)}, \(x\le0\), then the value of \(lim_{x\rightarrow 0}f(x)\) is equal to

\(lim_{n \rightarrow \infty}({1\over n^2}+{2\over n^2}+{3\over n^2}+..+{n\over n^2})\) is

\(lim_{x \rightarrow 0}{e^{tan \ x}-e^x\over tan x-x}=\)

The value of \(lim_{x \rightarrow 0}{sin x\over \sqrt{x^2}}\) is

The value of \(lim_{x\rightarrow k^-}x-\left\lfloor x \right\rfloor \) , where k is an integer is

At x \(={3\over 2}\) the function \(f(x)={|2x-3|\over 2x-3}\) is

Let a function f be defined by \(f(x)={x-|x|\over x}\) for x \(\neq\) 0 and f(0) = 2. Then f is

Consider the function f(x) = \(\sqrt{x},x\ge0.\) Does\(lim_{x\rightarrow0}f(x)\) exist?

In problems 1-6, using the table estimate the value of the limit.
\(lim_{x\rightarrow 2}{x-2\over x^2-x-2}\)

In problem, using the table estimate the value of the limit
\(lim_{x\rightarrow{-3}}{\sqrt{1-x}-2\over x+3}\)

In problem, using the table estimate the value of the limit
\(lim_{x\rightarrow0}{cos x-1\over x}\)

Suppose that the diameter of an animal’s pupils is given by \(f(x)={160x^{-0.4}+90\over 4x^{-0.4}+15},\) where x is the intensity of light and f(x) is in mm. Find the diameter of the pupils with minimum light.

Find the left and right limits of \(f(x)={x^2-4\over (x^2+4x+4)(x+3)}at \ x=-2\) .

Evaluate the following limits :\(lim_{x\rightarrow \infty}(1+{k\over x})^{m\over x} \)

Determine if f defined by \(f(x)=\left\{\begin{array}{ll} x^{2} \sin \frac{1}{x}, & \text { if } x \neq 0 \\ 0, & \text { if } x=0 \end{array} \text { is continuous in } \mathbb{R}\right.\)

Examine the continuity of the following: e^2x + x²

Find the points of discontinuity of the function f, where f(x) = {\(\begin{matrix} { x }^{ 3 }-3, & if\quad x\le 2 \\ { x }^{ 2 }+1, & if\quad x>2 \end{matrix}\)

Use the graph to find the limits (if it exists). If the limit does not exist, explain why?
\(lim_{x\rightarrow3}(4-x)\).

Use the graph to find the limits (if it exists). If the limit does not exist, explain why?
\(lim_{x\rightarrow1}(x^2+2)\)

Use the graph to find the limits (if it exists). If the limit does not exist, explain why?
\(lim_{x\rightarrow2}f(x)\)

Use the graph to find the limits (if it exists). If the limit does not exist, explain why?
\(lim_{x\rightarrow1}f(x)\)

Use the graph to find the limits (if it exists). If the limit does not exist, explain why?
\(lim_{x\rightarrow3}{1\over x-3}\)

Sketch the graph of f, then identify the values of x₀ for which \(lim_{x\rightarrow{x_o}}f(x)\) exists.
​\(f(x)=\begin{cases} { x^ 2 } ,\quad x \le 2 \\ 8-{ 2x } ,\quad 2 < x < 4 \\ { 4 } ,\quad x\ge 4 \end{cases}\)​

\(f(x)= \begin{cases}\sin x, & x<0 \\ 1-\cos x, & 0 \leq x \leq \pi \\ \cos x, & x>\pi\end{cases}\)

Calculate \(lim_{x\rightarrow0}{1\over (x^2+x^3)}\)