State the following Limit Laws. Difference Law

Determine the infinite limit. lim cot x x-->π-

Each limit represents the derivative of some function f at some number a. State such an f and a in each case. lim x6 - 64 / x - 2 x--->2

Make a table of values of f(x) for x close to 0 and guess the value of the limit.

Use a graph of the expression given below to estimate the value of $\lim _{x \rightarrow x} f(x)$ to one decimal place.

$$f(x)=\sqrt{3 x^2+8 x+6}-\sqrt{3 x^2+3 x+1}$$

Use a table of values of $f(x)$ to estimate the limit to four decimal places.

Find the exact value of the limit.

Match the graph of each function in (a)-(d) with the graph of its derivative in I-IV. Give reasons for your choices.

Find the limit, if it exists. If the limit does not exist, explain why.

$$\lim _{x \rightarrow -4}|x+4|$$

Estimate the value of lim x to 0 x/(1+3x)^1/2-1

Biologists have noticed that the chirping rate of crickets of a certain species is related to temperature, and the relationship appears to be very nearly linear. A cricket produces 113 chirps per minute at 70 degrees Fahrenheit and 173 chirps per minute at 80 degrees Fahrenheit.

Find a linear equation that models the temperature T as a function of the number of chirps per minute N.

The Sierpinski carpet is constructed by removing the center one-ninth of a square of side 1 , then removing the centers of the eight smaller remaining squares, and so on. (The figure shows the first three steps of the construction.) Show that the sum of the areas of the removed squares is 1 . This implies that the Sierpinski carpet has area 0 .

Use a table of values of $f(x)$ to estimate the limit to four decimal places.

Match the graph of each function in (a)-(d) with the graph of its derivative in I-IV. Give reasons for your choices.

Find the limit or show that it does not exist. lim tan-1 (In x) x-->0+

Differentiate the function. $R(a)=(3 a+1)^{2}$