Analyzing Functions Explained by Our Experts

Find the critical points of a function $f (x, y) = x y^{2} - 3 x^{2} - y^{2} - 2 x + 2$

Josh Sizemore 2021-12-13

When should I use brackets or parenthesis in finding domain or range?

smileycellist2 2021-10-15

Find the critical points of the following functions.
$f (x, y) = - 4 x^{2} + 8 y^{2} - 3$

ankarskogC 2021-10-14

Which of the following is a verbal version of the Product Law (assuming the limits exist)?
(a) The product of two functions has a limit.
(b) The limit of the products the product of the limits.
(c) The product of a limitis a product of functions.
(d) A limit produces a product of functions.

amanf 2021-10-14

What do the $lim_{h \to 0} \frac{\sin h}{h}$ and $lim_{h \to 0} \frac{\cosh - 1}{h}$ have to do with the derivatives of the sine and cosine functions? What are the derivatives of these functions?

Nannie Mack 2021-10-14

Techniques of Integration: Integration by Parts, Products of Powers of Trigonometric Functions
Use integration by parts to integrate functions.
Integrate products of powers of trigonometric functions.
Evaluate
$I = \int x \sin 3 x d x$

Alyce Wilkinson 2021-10-14

Find the critical points of the following functions.
$f (x, y) = x^{4} + y^{4} - 4 x - 32 y + 10$

Globokim8 2021-10-13

Find the critical points of the following functions.Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, a local minimum,or a saddle point. If the Second Derivative Test is inconclusive,determine the behavior of the function at the critical points.
$f (x, y) = \sin$ $(2 π x) \cos (π y)$ , for $| x | \leq \frac{1}{2}$ and $| y | \leq \frac{1}{2}$

Chesley 2021-10-13

In this problem, use the following functions:
$a {(x}) = \sqrt{x}$
$h {(x}) = x^{2}$
$n {(x}) = e^{x}$
$r {(x}) = x + 7$
$p {(x}) = \frac{1}{x}$
$g {(x}) = 5 x$
Each function below is some composition of the functions above. For example, the function $y = {{(x + 7})}^{2}$ is the composition $h {(r {(x})})$
For each function below, write the simplest composition using two of the functions from the given list.
$5 {(\frac{1}{x}}) =$
$5 (e^{x}) =$
$\sqrt{{(x + 7})} =$
The next two functions are compositions of three different functions from the given list.
${{({(\frac{1}{x}}) + 7})}^{2} =$
$e^{{(x^{2}})} + 7 =$

sagnuhh 2021-10-13

Find the critical points of the following functions.Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, a local minimum,or a saddle point. If the Second Derivative Test is inconclusive,determine the behavior of the function at the critical points.
$f (x, y) = {(4 x - 1)}^{2} + {(2 y + 4)}^{2} + 1$

iohanetc 2021-10-13

By examining the appropriate limits, ascertain the final behavior of the following transcendental functions. The associated graph is then simply sketched, with any asymptotes indicated.
$f (x) = 2^{x}$

vestirme4 2021-10-12

Analyzing critical points.
Use the Second Derivative Test to classify the critical points of $f (x, y) = x^{2} + 2 y^{2} - 4 x + 4 y + 6$ .

Tyra 2021-10-12

Inverse Trigonometric Functions Are the derivatives of the inverse trigonometric functions algebraic or transcendental functions? Explain.

Nannie Mack 2021-10-12

What are the derivatives of the six basic hyperbolic functions? What are the corresponding integral formulas? What similarities do you see here to the six basic trigonometric functions?

postillan4 2021-10-12

What do the limits $lim_{h \to 0} \frac{\sin h}{h}$ and $lim_{h \to 0} \frac{\cos h - 1}{h}$ have to do with the derivatives of the sine and cosine functions? What are the derivatives of these functions?

Anonym 2021-10-12

To determine
(1) If f and g are both even functions, whether $f + g$ is even?
(2) If f and g are both odd functions, whether $f + g$ is odd?
(3) If f is even and g is odd function, what will $f + g$ ?

Tyra 2021-10-11

Analizing the polynomial
$y = (x - 1) (3 x - 2) (x + 3)$
a) Determine the roots of the polinomial
b) Determine the end behaviors
c) Determine how many turning points

Brittney Lord 2021-10-11

Techniques of Integration: Integration by Parts, Products of Powers of Trigonometric Functions
Use integration by parts to integrate functions.
Integrate products of powers of trigonometric functions.
Evaluate
$\int \sin^{4} θ \cos^{2} θ d θ$

Cabiolab 2021-10-10

Find functions fand g such that
$h = g \circ f$
(Note: The answer is not unique. Enter your answers as a comma-separated list of functions. Use non- identity functions for fand g.)
$h (x) = {(5 x^{2} - 8)}^{- 3}$

ankarskogC 2021-10-09

Describe the First Derivative Test in your own words.

As you are analyzing function completely ap problems, you will need clear examples that will contain detailed answers to your questions. Since there will be more than equations alone, the most important is to provide analysis. The same relates to analyzing function packet answers that can be either answered based on instructions (as in many replies below) as well as generated by various software. Reading through both examples will help you to see how calculus implements functions and what aspects of analysis must be provided to receive complete answers.

Calculus 1

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