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3 years ago

Please help! Need answered! Please and thank you.

Mathematics

2 answers:

ANEK [815]3 years ago

8 0

Answer: (a) 5

Step-by-step explanation:

$\lim_{x \to 2} 5$ means what is the y-value when x = 2 .

The given equation is: y = 5 so the y-value is 5 for all values of x

Answer: (c) 13

Step-by-step explanation:

f(x) = x² + 5x

f'(x) = 2x + 5

f'(4) = 2(4) + 5

= 8 + 5

= 13

Answer: (c) 2

Step-by-step explanation:

The question is asking what the y-value is when x = -2. The graph shows that the coordinate (-2, 2) is on the curve. So, when x = -2, y = 2.

Elan Coil [88]3 years ago

5 0

Answer:

lim x→2 5 =5

The slope is 13

lim x→-2 x^2 -2 =2

Step-by-step explanation:

lim x→2 5 =5

The limit of a constant is the constant

f(x) = x^2 +5x

We need to take the derivative

f'(x) = 2x+5

Then evaluate the derivative at x=4 (4,36)

f'(4) = 2*4 +5

= 8+5

= 13

The slope is 13

lim x→-2 x^2 -2 =2

Looking at the graph, the value of the function at -2 is about 2

We can also calculate it (-2)^2 -2 = 4-2 = 2

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3 years ago

5(x+1)=20 What is is the answer?

Ilia_Sergeevich [38]

Steps to solve:

5(x + 1) = 20

~Distributive property

5x + 5 = 20

~Subtract 5 to both sides

5x + 5 - 5 = 20 - 5

~Simplify

5x = 15

~Divide 5 to both sides

5x/5 = 15/5

~Simplify

x = 3

Best of Luck!

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3 years ago

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3 years ago

Four-fifths the sum of twice a number and nine is equal to negative

wlad13 [49]

Answer:

The number should be -22

Step-by-step explanation:

4/5(2x + 9) = -28

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2 years ago

Use the Chain Rule (Calculus 2)

atroni [7]

1. By the chain rule,

$\dfrac{\mathrm dz}{\mathrm dt}=\dfrac{\partial z}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial z}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}$

I'm going to switch up the notation to save space, so for example, $z_x$ is shorthand for $\frac{\partial z}{\partial x}$ .

$z_t=z_xx_t+z_yy_t$

We have

$x=e^{-t}\implies x_t=-e^{-t}$

$y=e^t\implies y_t=e^t$

$z=\tan(xy)\implies\begin{cases}z_x=y\sec^2(xy)=e^t\sec^2(1)\\z_y=x\sec^2(xy)=e^{-t}\sec^2(1)\end{cases}$

$\implies z_t=e^t\sec^2(1)(-e^{-t})+e^{-t}\sec^2(1)e^t=0$

Similarly,

$w_t=w_xx_t+w_yy_t+w_zz_t$

where

$x=\cosh^2t\implies x_t=2\cosh t\sinh t$

$y=\sinh^2t\implies y_t=2\cosh t\sinh t$

$z=t\implies z_t=1$

To capture all the partial derivatives of $w$ , compute its gradient:

$\nabla w=\langle w_x,w_y,w_z\rangle=\dfrac{\langle1,-1,1\rangle}{\sqrt{1-(x-y+z)^2}}}=\dfrac{\langle1,-1,1\rangle}{\sqrt{-2t-t^2}}$

$\implies w_t=\dfrac1{\sqrt{-2t-t^2}}$

2. The problem is asking for $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}$ . But $z$ is already a function of $x,y$ , so the chain rule isn't needed here. I suspect it's supposed to say "find $\frac{\partial z}{\partial s}$ and $\frac{\partial z}{\partial t}$ " instead.