1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
cluponka [151]
3 years ago
9

Find lim PLEASE I NEED HELP ASAP !!!!

Mathematics
1 answer:
stira [4]3 years ago
5 0

Computing the limit directly:

\displaystyle\lim_{h\to0}\frac{f(2+h)-f(2)}h=\lim_{h\to0}\frac{((2+h)^2+(2+h)+1)-7}h\\\displaystyle=\lim_{h\to0}\frac{5h+h^2}h\\=\displaystyle\lim_{h\to0}(5+h)=\boxed{5}

Alternatively, you can recognize the limit as being equivalent the derivative of <em>f(x)</em> at <em>x</em> = 2, in which case differentiating and plugging in 2 gives

<em>f'(x)</em> = 2<em>x</em> + 1   =>   <em>f'</em> (2) = 5

You might be interested in
Shirts are on sale 20% off! The original price of the shirt was $28.50. How
loris [4]

Answer: im not sure

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Thomas needs to buy a cardboard sheet that will allow him to make his 224 in 3 box. To help construct the box, he decided to cut
Slav-nsk [51]

Answer:

Part 1; The volume of the box Thomas wants to make is 224 = 2·w² + 12·w

Part 2; The zeros for the equation of the function, are w = -14, or w = 8

Part 3

The width of the box is 8 inch

The length of the box, is 14 inches

The height of the box, is given as 2 inches

Part 4

Please find attached the graph of the function

Step-by-step explanation:

Part 1

The volume of the box Thomas wants to make, V = 224 in.³

The dimensions he cuts out from the length and width = 2 in² each

The length of the box = 6 inches + The width of the box

Let <em>l</em> represent the length of the box and let <em>w</em> represent the width of the box, we have;

l = 6 + w

The height of the box, h = The length of the cut out square = 2 inches

The volume of the box, V = Length, l × Width, w × Height, h

∴ V = l × w × h

l = 6 + w, h = 2

∴ V = (6 + w) × w × 2

V = 2·w² + 12·w,

The equation of the volume of the box, V = 2·w² + 12·w, where, V = 224

∴ 224 = 2·w² + 12·w

Part 2

The zeros of the equation for the volume of the box, V = 2·w² + 12·w, where, V = 224 are found as follows;

V = 224 = 2·w² + 12·w

∴ 2·w² + 12·w - 224 = 0

Dividing by 2 gives;

(2·w² + 12·w - 224)/2 = w² + 6·w - 112 = 0

∴ (w + 14) × (w - 8) = 0

The zeros for the equation of the function, are w = -14, or w = 8

Part 3

We reject the value, w = -14, therefore, the width of the box, w = 8 inch

The length of the box, l = 6 + w

∴ l = 6 + 8 = 14

The length of the box, l = 8 inches

The height of the box, <em>h</em>, is given as h = 2 inches

Part 4

The graph of the function created with MS Excel is attached

4 0
3 years ago
Name the place value to which each number was rounded 0.982to 0.98
Kryger [21]
The Hundredths place because 2 is in the thousandths place. 5 or more change the score, 4 or less let it rest. 8 remained the same because 2 is less than 4.
8 0
3 years ago
N
sergeinik [125]

Answer: (0,4)

Step-by-step explanation:

3 0
2 years ago
A right triangle has a side length of 12 m and a side length of 15 m. Find the length of the missing hypotenuse. Rounded to the
kolezko [41]

Answer:

19.2

Step-by-step explanation:

12 squared + 15 squared= C squared

144 + 225 = C squared

369 = C squared

Do square root of 369, which is

19.2

7 0
3 years ago
Other questions:
  • The least squares regression line minimizes the sum of the:
    6·1 answer
  • Please help me with the following questions. Thanks in advance!
    8·1 answer
  • What is the answer of two plus two
    13·2 answers
  • If all the dimensions of a triangle are doubled,the area of the triangle will be doubled,too
    12·2 answers
  • 6(2x-11)+15=21
    15·2 answers
  • I need help with this.
    11·1 answer
  • Each vertex of the polygon shown below forms a right angle. The side measurements given are in inches.
    6·1 answer
  • Mary had 33 pennies in her pocket. She spent 25 of the pennies. Then she found 2 pennies and put them into her pocket. Which sho
    15·2 answers
  • 45/14 as a decimal rounded to the nearest 10th
    14·1 answer
  • Can YALL HELP ME WITH THIS
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!