All categories

2 years ago

If lim(x->3) f(x)=7, which of the following must be true?

Mathematics

1 answer:

fenix001 [56]2 years ago

5 0

If lim(x->3) f(x)=7, then f(3) = 7.

You might be interested in

Which coordinate pairs make the equation x-9y=12 true?

asambeis [7]

Answer:

(12,0) and (3, -1) and (0,-4/3)

Step-by-step explanation:

To find if a point makes an equation true, just substitute its x and y values in in the equation and simplify.

1) Let's test the point (12,0). Substitute 12 for x and 0 for y in the equation:

$x-9y=12\\(12)-9(0)=12\\12-0=12\\12=12$

12 does equal 12, so (12,0) makes the equation true.

2) Let's test the point (0, 12). Substitute 0 for x and 12 for y in the equation:

$x-9y=12\\(0)-9(12) = 12\\0-108 = 12\\-108 = 12$

However, -108 does not equal 12, so (0,12) does not make the equation true.

3) Let's test the point (3, -1). Substitute 3 for x and -1 for y in the equation:

$x-9y=12\\(3)-9(-1) = 12\\3 + 9 = 12\\12 = 12$

12 does equal 12, so (3, -1) makes the equation true.

4) Let's test the point (0, -4/3). Substitute 0 for x and -4/3 for y in the equation:

$(0) -9(-\frac{4}{3} ) = 12\\0 + \frac{36}{3} = 12\\0 + 12 = 12 \\12 = 12$

12 does equal 12, so (0, -4/3) makes the equation true.

8 0

3 years ago

What is the limit of the infinite series ? ∑n=1∞(3n^5/6n^6+1)

yulyashka [42]

I don’t know sorry mansisnsiwhe sha

8 0

3 years ago

What is the inverse of f(x)=(x+6)2 for x≥–6 where function g is the inverse of function f? g(x)=x√−6, x≥0 g(x)=x−6−−−−√, x≥6 g(x

avanturin [10]

Answer:

$g(x)=\sqrt{x}-6$ , x>=0

Step-by-step explanation:

$f(x)=(x+6)^2$

To find the inverse function , replace f(x) by y

$y=(x+6)^2$

Replace x with y and y with x

$x=(y+6)^2$

Solve the equation for y

take square root on both sides

$+\sqrt{x} =y+6$

Now subtract 6 from both sides

$+\sqrt{x}-6=y$

replace y with g(x)

$g(x)=\sqrt{x}-6$

8 0

3 years ago

A concession stand at an athletic event is trying to determine how much to sell cola and iced tea for in order to maximize reven

Cerrena [4.2K]

Solution :

Demand for cola : 100 – 34x + 5y

Demand for cola : 50 + 3x – 16y

Therefore, total revenue :

x(100 – 34x + 5y) + y(50 + 3x – 16y)

R(x,y) = $100x-34x^2+5xy+50y+3xy-16y^2$

$R(x,y) = 100x-34x^2+8xy+50y-16y^2$

In order to maximize the revenue, set

$R_x=0, \ \ \ R_y=0$

$R_x=\frac{dR }{dx} = 100-68x+8y$

$R_x=0$

$68x-8y=100$ .............(i)

$R_y=\frac{dR }{dx} = 50-32x+8y$

$R_y=0$

$8x-32y=-50$ .............(ii)

Solving (i) and (ii),

4 x (i) ⇒ 272x - 32y = 400

(ii) ⇒ (-) 8x - 32y = -50

264x = 450

∴ $x=\frac{450}{264}=\frac{75}{44}$

$y=\frac{175}{88}$

So, x ≈ $ 1.70 and y = $ 1.99

R(1.70, 1.99) = $ 134.94

Thus, 1.70 dollars per cola

1.99 dollars per iced ted to maximize the revenue.

Maximum revenue = $ 134.94

4 0

3 years ago

What is the 3rd term in the sequence?

makvit [3.9K]

Answer:

Step-by-step explanation:

To find the third term substitute n = 3 into the n th term formula

a(3) = $\frac{3}{2}$ $(-2)^{3-1}$

= $\frac{3}{2}$ $(-2)^{2}$

= $\frac{3}{2}$ × 4 = 6

4 0

2 years ago