I need to write an expression to represent the volume of this shape

Recall some limit properties…

• limits distribute over sums:

[tex]\displaystyle \lim_{x\to c}(f(x)+g(x)) = \lim_{x\to c}f(x)+\lim_{x\to c}g(x)[/tex]

• limits distribute over products:

[tex]\displaystyle \lim_{x\to c}(f(x)\times g(x)) = \lim_{x\to c}f(x)\times\lim_{x\to c}g(x)[/tex]

• limits distribute over quotients, provided that the denominator doesn't approach 0 :

[tex]\displaystyle\lim_{x\to c}\frac{f(x)}{g(x)} = \frac{\displaystyle\lim_{x\to c}f(x)}{\displaystyle\lim_{x\to c}g(x)}[/tex]

• if f(x) is continuous at x = c, then the limit "passes through" a composition:

[tex]\displaystyle \lim_{x\to c}f(g(x)) = f\left(\lim_{x\to c}g(x)\right)[/tex]

# # #

(a) This limit is 2. At x = 2, we have f (2) = 1, but from either side of x = 2, we see f(x) approaching the point (2, 2). So

[tex]\displaystyle \lim_{x\to 2}(f(x)+g(x)) = \lim_{x\to2}f(x)+\lim_{x\to2}g(x) = 2+0 = 2[/tex]

(b) This limit does not exist. We would have

[tex]\displaystyle \lim_{x\to1}(2f(x)-3g(x)) = 2\lim_{x\to1}f(x)-3\lim_{x\to1}g(x)[/tex]

but g(x) approaches 2 from the left of x = 1, and g(x) approaches 1 from the right of x = 1. The one-sided limits don't match, so the two-sided limit doesn't exist.

(c) This limit is 0. It looks like f(x) passes through the origin, while g(x) ≈ 3/2 at x = 0. So

[tex]\displaystyle\lim_{x\to0}f(x)g(x) = \lim_{x\to0}f(x)\times\lim_{x\to0}g(x)=0\times\frac32 = 0[/tex]

(d) This limit does not exist since

[tex]\displaystyle \lim_{x\to-1}g(x)=0[/tex]

(e) This limit is 16. Nothing tricky here, just use the same property as in (c).

[tex]\displaystyle\lim_{x\to2}x^3f(x) = \lim_{x\to2}x^3\times\lim_{x\to2}f(x) = 8\times2=16[/tex]

(f) This limit is 1. f(x) is continuous at x = 1, while g(x) approaches 2 from the left.

[tex]\displaystyle\lim_{x\to1^-}f(g(x)) = f\left(\lim_{x\to1^-}g(x)\right) = f(2) = 1[/tex]

Answers:

The logarithmic function f(x) = ln(x) is the natural logarithmic function and has base  e  

=======================================

Explanation:

The ln(x) or Ln(x) is the natural log function. The order of L and n is backwards compared to "natural log", but you can think of it "log that is natural" or something along those lines.

The Ln(x) function is of the form [tex]\log_b(x)[/tex] where the base b is the special constant e = 2.718... (this constant is similar to pi = 3.14...)

Answer: [tex]2\sqrt{3}[/tex]

Step-by-step explanation:

First, start by expanding the expression to this

[tex]\frac{6}{\sqrt{3}} * \frac{\sqrt{3} }{\sqrt{3} }[/tex]

Then multiply the fractions by numerators and denominators (separately)

[tex]\frac{6*\sqrt{3} }{\sqrt{3}*\sqrt{3} }[/tex]

It results in this, the radical 3 * radical 3 get rid of the square root and result in 3

[tex]\frac{6\sqrt{3} }{3}[/tex]

Reduce the fraction by dividing the 6 by 3 so your solution is

[tex]2\sqrt{3}[/tex]

Answer:

UW = 67

Step-by-step explanation:

In order to find UW, we need to add UV and VW because them together makes the entire line, also known in this problem as UW. This is our equation:

UV + UV = UW

This is the equation if you plug the numbers:

19 + 4x - 20 = 6x - 35

Combine like terms to make it easier to do the math:

4x - 1 = 6x - 35

Then do the math:

(4x - 4x) -1 = (6x - 4x) - 35

-1 = 2x - 35

(-1 + 35) = 2x (- 35 + 35)

34 = 2x

34/2 = 2x/2

x = 17

Then you plug in x for the UW expression:

6x - 35

6(17) - 35

102 - 35

67

UW = 67

Answer:

1) D: -8 < x ≤ 2, R: -4 ≤ y ≤ 11.

2) D: -8 ≤ x ≤ -3 U 2 ≤ x < ♾️,

R: -6 ≤ y ≤ -5 U -3 ≤ y < ♾️.

Answer:

143.5

Step-by-step explanation:

4lnx=20

lnx=5

lnx= logeX

logeX=5

x=e^5

that is approximately equal to 2.7^5= 143.5

Answer:

x=148.4

Step-by-step explanation:

B. -4/6

Step-by-step explanation:

5x+x=-4

6x=-4

x=-4/6

Answer:

Step-by-step explanation:

If you are solving for x then you should get something like this

A 5x-2+x=x- 4 B. 5x+x=x-4

6x-2=-4. 6x=x-4

6x-2-x=-4. 6x-x=-4

5x-2+2=-4+2. 5x=-4

5x/5=-2/5. 5x/5=-4/5

x=-2/5. x=-4/5

I hope this helped you out!

Answer:

Try h=(1-6πs)/6π

Step-by-step explanation:

That's the same answer in another format

Answer:

(10, -9)

Step-by-step explanation:

Xs = 5 -(0-5) = 5+5 = 10

Ys = -2 -(5-(-2)) = -2 - 7 = -9

so, the coordinates of point S => (10, -9)

Answer:

Step-by-step explanation:

Use midpoint formula and assume S(x, y):

Answer:

answer is in photo.

Green one is main answer and blue one is formula

Answer:

fraction of blue beads = 7/(4+7)

= 7/11

Answer:

3:5

Step-by-step explanation:

find a common numeral

Answer:

Step-by-step explanation:

Answer:

30 caps can be bought

Step-by-step explanation:

[tex]{ \sf{Rs.800 = (10 \times 12) \: caps}} \\ { \sf{Rs.200 = ( \frac{200 \times 10 \times 12}{800}) \: caps}} \\ \\ { \sf{ = 30 \: caps}}[/tex]

Answer:

common ratio=0.5, a1= 0.08

Step-by-step explanation:

r=a3/a2

r=a4/a3

compare both we get:

a3/a2=a4/a3

subtitute a2=0.04 and a4=1

a3/0.04=1/a3

(a3)^2=0.04*1

(a3)^2=0.04

taking square root in both sides

a3=0.02

For r, r=a3/a2

subtitute a3 and a2 above

r=0.02/0.04

r=0.5 common ratio

For a1

r=a2/a1

0.5=0.04/a1

a1=0.04/0.5

a1=0.08

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

The first term of the geometric sequence is 0.08.

The common ratio of the geometric sequence is 1/0.02.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

We have,

Geometric sequence:

The second term = 0.04

The fourth term = 1

In a geometric sequence the nth term is given as:

[tex]a_{n}[/tex] = [tex]a_1 r^{n-1}[/tex]

Second term = 0.04

[tex]a_2[/tex] = 0.04

[tex]a_1 r^1 = 0.04[/tex]

[tex]a_1r[/tex] = 0.04 _____(1)

Fourth term = 1

[tex]a_4 = 1[/tex]

[tex]a_1 r^3[/tex] = 1 _____(2)

From (1) and (2) we get,

0.04/r = 1/r³

r³ = r / 0.04

r² = 1/0.04

r = 1/0.02 ____(3)

Putting (3) in (1) we get

[tex]a_1[/tex] = 0.04 x 0.02 = 0.08

Thus,

The first term of the geometric sequence is 0.08.

The common ratio of the geometric sequence is 1/0.02.

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Answer:

[tex]x^{14}[/tex]

Step-by-step explanation:

[tex]x^{5}[/tex] × [tex]x^{3}[/tex] × [tex]x^{6}[/tex]

[tex]x^{5+3+6}[/tex]

[tex]x^{14}[/tex]

Answer:

[tex] \frac{1 - 2 \sqrt{x} + x }{1 - x} [/tex]

Step-by-step explanation:

[tex] \frac{1 - \sqrt{x} }{1 + \sqrt{x} } [/tex]

Rationalize the denominator by multiplying by it conjugate.

[tex] \frac{1 - \sqrt{x} }{1 + \sqrt{x} } \times \frac{1 - \sqrt{x} }{1 - \sqrt{x} } = \frac{1 - 2 \sqrt{x} + x}{1 - x} [/tex]

Answer:

a = 6

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

a^2 + 8^2 = 10 ^2

a^2 +64 = 100

a^2 = 100 -64

a^2 = 36

Take the square root of each side

sqrt(a^2) = sqrt(36)

a = 6

Answer:

huh

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

By convention, it is C.

B is irrational but still real

D is irrational but still real

A is an integer which is real.

Answer: 4 + 9i

On edge2020.

Answer:

Step-by-step explanation:

A = [tex]\frac{x+y}{2}[/tex]

2A = x + y

y = 2A - x

Answer:

[tex]{ \bf{ \bar {MN}} \: means \: length \: between \: M \: and \: N}[/tex]

MN means line joining point M to point N.

Answer:

672

Step-by-step explanation:

Given: 8 pizza hut's sold a total of 5,376 pizzas

Each pizza hut sold the same amount of pizzas

So number of pizzas sold from 1 pizza hut = 5376/8 = 672

Answer:

x = -5  ±4sqrt(3)

Step-by-step explanation:

(x + 5)^2 = 48

Take the square root of each side

sqrt((x + 5)^2) = ±sqrt(48)

x+5 = ±sqrt(16*3)

x+5 = ±4sqrt(3)

Subtract 5 from each side

x = -5  ±4sqrt(3)

Answer:

Step-by-step explanation:

Answer:

7.3

Step-by-step explanation:

The length of AB is found using the distance formula

We need to know the coordinates of A and B

A = (-5,-4) and B = (-3,3)

The distance is

d = sqrt ( (y2-y1)^2 + (x2-x1)^2)

   = sqrt( (3 - -4)^2 +(-3 - -5)^2)

   = sqrt( (3+4)^2 +(-3+5)^2)

   = sqrt(7^2+2^2)

   = sqrt(49+4)

  = sqrt(53)

  =7.280109889

To the nearest hundredth

 =7.3

Answer:

52

Step-by-step explanation:

AB is the hypotenuse of the right triangle

sin34 = opp/hyp = 29/hyp

hyp = 29/sin34 = 51.860457849...

Answer:

[tex]let \: |ab| \: be \: x \\ \\ \frac{ \sin(90) }{x} = \frac{ \sin(34) }{29} \\ x \sin(34) = 29 \sin(90) \\ x = \frac{29 \sin(90) }{ \sin(34) } \\ x = 51.86(2.d.p) \\ |ab| = 51.86[/tex]

The required simplified value of the given expression is 16x¹². Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
=(2x³)⁴

As we know that,
[xᵃ]ᵇ = xᵃˣᵇ

So,
(2x³)⁴ = 2⁴x³ˣ⁴
        = 16x¹²

Thus, the required simplified value of the given expression is 16x¹².

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