Let f(x) = x2 + 8x - 2, find lim f(x). X 2

Jason planted and staked a tree. The stakes are 21 ft from the base of the tree. They are connected to wires that attach to the

bekas [8.4K]

20ft huhuhquanjqbqjnqjqnuqhuq qbquqhuqhqhquhquqhuqhiq

4 0

3 years ago

Which of the following is the simplified form of ^7 radical x • ^7 radical x • ^7 radical x

schepotkina [342]

For this case we must find an expression equivalent to:

$\sqrt [7] {x} * \sqrt [7] {x} * \sqrt [7] {x}$

By definition of properties of powers and roots we have:

$\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}$

So, rewriting the given expression we have:

$x ^ {\frac {1} {7}} * x ^ {\frac {1} {7}} * x ^ {\frac {1} {7}} =$

To multiply powers of the same base we put the same base and add the exponents:

$x ^ {\frac {1} {7} + \frac {1} {7} + \frac {1} {7}} =\\x ^ {\frac {3} {7}}$

Answer:

Option 1

6 0

3 years ago

Read 2 more answers

Compute the second partial derivatives ∂2f ∂x2 , ∂2f ∂x ∂y , ∂2f ∂y ∂x , ∂2f ∂y2 for the following function. f(x, y) = 2xy (x2 +

blsea [12.9K]

Answer with step-by-step explanation:

We are given that a function

$f(x,y)=2xy(x^2+y^2)^2$

Differentiate partially w.r.t x

Then, we get

$\frac{\delta f}{\delta x}=2y(x^2+y^2)^2+8x^2y(x^2+y^2)=(x^2+y^2)(2x^2y+2y^3+8x^2y)=2(5x^2y+y^3)(x^2+y^2)$

Differentiate again w.r.t x

$\frac{\delta^2f}{\delta x^2}=2(10xy)(x^2+y^2)+4x(5x^2y+y^3)=20x^3y+20xy^3+20x^3y+4xy^3=40x^3y+24xy^3$

Differentiate function w.r.t y

$\frac{\delta f}{\delta y}=2x(x^2+y^2)^2+2xy\times 2(x^2+y^2)\times 2y$

$\frac{\delta f}{\delta y}=(x^2+y^2)(2x^3+2xy^2+8xy^2)=2(x^2+y^2)(x^3+5xy^2)$

Again differentiate w.r.t y

$\frac{\delta^2f}{\delta x^2}=2(2y)(x^3+5xy^2)+20xy(x^2+y^2)=4x^3y+20xy^3+20x^3y+20xy^3=24x^3y+40xy^3$

Differentiate partially w.r.t y

$\frac{\delta^2f}{\delta y\delta x}=2(2y(5x^2y+y^3)+(x^2+y^2)(5x^2+3y^2))=10x^4+36x^2y^2+10y^4$

$\frac{\delta^2f}{\delta y\delta x}=10x^4+36x^2y^2+10y^4$ $\frac{\delta^2f}{\delta x\delat y}=2(2x(x^3+5xy^2)+(3x^2+5y^2)(x^2+y^2))=10x^4+36x^2y^2+10y^4$

$\frac{\delta^2f}{\delta x\delat y}=10x^4+36x^2y^2+10y^4$

Hence, if f(x,y) is of class $C^2$ (is twice continuously differentiable), then the mixed partial derivatives are equal.

i.e $\frac{\delta^2f}{\delta y\delta x}=\frac{\delta^2f}{\delta x\delta y}$

8 0

4 years ago

The mean of four numbers is 61. If three of the numbers are 47,65, and 77, what is the fourth number?

bixtya [17]

ANSWER

my answer is in the photo above

6 0

3 years ago

Jacob's Boat Rentals charges a one-time fee plus a $5 hourly rate to rent a boat. The cost to rent a boat for 2 hours is $25 and

maks197457 [2]

Hi there! The answer is $15

Let the one-time fee be represented by X.
The total cost of hiring a boat for 2 hours is X + $5 per hour × 2 hours = X + $10

The total cost can also be expressed as $25.
Now we can set up an equation.
X + 10 = 25

Subtract 10.
X = 15

Therefore, the one-time fee to rent a boat is $15.

We can check this by plugging in the data for the rent of 3 hours.
$15 + $5 per hour × 3 hours =
$15 + $15 = $30, which is the correct answer.

In short:
The answer is $15
~ Hope this helps you!

7 0

3 years ago