91影视

Calculate each of the limits in Exercises $49-64$. Some of these limits are made easier by considering the logarithm of the limit first, and some are not.

$\underset{x鈫�2^{+}}{\lim }(x-2{)}^{x^2-4}$.

For each graph of f in Exercises 49鈥�52, explain why f satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b] and approximate any values c 鈭� (a, b) that satisfy the conclusion of the Mean Value Theorem.

In Exercises 52-55, Linda is bored and decides to pour an entire container of salt into a pile on the kitchen floor. She pours 3 cubic inches of salt per second into a conical pile whose height is always two-thirds of its radius.

How fast is the radius of the conical salt pile changing when the radius of the pile is $2$inches?

For each sign chart for $f^{\text{'}}$in Exercises 51鈥�56, sketch possible graphs of both $f^{\text{'}}$and $f$. On each sign chart, unlabeled tick-marks are locations where $f^{\text{'}}\left(x\right)$is zero and $x$-values where $f^{\text{'}}\left(x\right)$does not exist are indicated by tick-marks labeled 鈥淒NE.鈥�

Calculate each of the limits in Exercises $49-64$. Some of these limits are made easier by considering the logarithm of the limit first, and some are not.

$\underset{x鈫�0^{+}}{\lim }{\left(x^2+1\right)}^x$.

Suppose you have a $10$-inch length of wire that you wish to cut and form into shapes. In the given below question, you will determine how to cut the wire to minimize or maximize the area of the resulting shapes.

Suppose you wish to make one cut in the wire and use the two pieces to form a square and an equilateral triangle. Determine how to cut the wire so that the combined area is (a) as small as possible and (b) as large as possible.

Suppose you have a $10$-inch length of wire that you wish to cut and form into shapes. In the given below question, you will determine how to cut the wire to minimize or maximize the area of the resulting shapes.

Suppose you wish to make one cut in the wire and use the two pieces to form a circle and an equilateral triangle. Determine how to cut the wire so that the combined area of these two shapes is (a) as small as possible and (b) as large as possible.

For each set of sign charts in Exercises 53鈥�62, sketch a possible graph of$f.$

Use a sign chart for$f\text{'}\text{'}$ to determine the intervals on which each function f in Exercises 41鈥�52 is concave up or concave down, and identify the locations of any inflection points. Then verify your algebraic answers with graphs from a calculator or graphing utility

$f\left(x\right)=3\cos \left(\frac{蟺}{2}x\right)+5$

Calculate each of the limits in Exercises 49鈥�64. Some of these limits are made easier by considering the logarithm of the limit first, and some are not.

$\underset{x鈫�1}{\lim }{x}^{\frac{1}{x-1}}$