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
Hunter-Best [27]
3 years ago
7

Find the limit if it exists lim x→0 sqrtx+7-sqrt7 over x

Mathematics
1 answer:
Triss [41]3 years ago
6 0

Answer:

\frac{1}{ 2\sqrt{7} }

Step-by-step explanation:

\lim_{x\to 0}  \frac{ \sqrt{x + 7}  -  \sqrt{7} }{x}  \\  \\  = \lim_{x\to 0}  \frac{( \sqrt{x + 7}  -  \sqrt{7}) }{x}  \times  \frac{( \sqrt{x + 7}   +   \sqrt{7}) }{( \sqrt{x + 7}   +  \sqrt{7}) }  \\  \\   = \lim_{x\to 0}  \frac{( \sqrt{x + 7} )^{2}  -  (\sqrt{7})^{2}  }{x( \sqrt{x + 7}   +  \sqrt{7})}  \\  \\   = \lim_{x\to 0}  \frac{( {x + 7}  -  {7}) }{x( \sqrt{x + 7}   +  \sqrt{7})}   \\  \\ = \lim_{x\to 0}  \frac{ {\cancel x}}{\cancel x( \sqrt{x + 7}   +  \sqrt{7})} \\  \\ = \lim_{x\to 0}  \frac{ {1}}{\sqrt{x + 7}   +  \sqrt{7}}  \\  \\  =  \frac{1}{ \sqrt{0 + 7} +  \sqrt{7}  } \\  \\  =  \frac{1}{ \sqrt{7} +  \sqrt{7}  }  \\  \\  =  \frac{1}{ 2\sqrt{7} }

You might be interested in
In a week, 15 hens laid 75 eggs. what is the unit rate for eggs per hen?
yarga [219]
75 divided by 15 is 5. 5 eggs per hen
8 0
3 years ago
6. Matthew is planning to build a right triangular
saul85 [17]
The answer to this question will be B
8 0
3 years ago
Find slope of both lines and determine if parallel, perpendicular or neither
Oxana [17]

Answer:

Parallel

Step-by-step explanation:

y=5x+10

y=5x-15

3 0
2 years ago
. Anne is pushing a wheelbarrow filled with mulch to place in her garden. She is pushing the wheelbarrow with a force of 70 N at
Kruka [31]

<u>Answer:</u>

When Anne pushes the wheelbarrow 25 meters the work done is 1120 joules

<u>Solution:</u>

We know \text { Work }(\mathrm{W})=\text { Force }(\mathrm{F})\times\text { Distance (D) }

Anne is pushing the wheelbarrow with a force of 70 N at an angle of 50^{\circ} with the horizontal

So the force of Anne will be F=70 \cos 50^{\circ}=(70 \times 0.64)=44.8 \mathrm{N}

She pushes the wheelbarrow 25 meter, So D = 25 meters

So, the work,F\times D=(44.8 \times 25)=1120 \text { Joules }

Anne has done total 1120 joules work.

4 0
3 years ago
Rewrite using a single positive exponent
Korolek [52]

Answer:

9³

Step-by-step explanation:

We need to find the value of \dfrac{9^5}{9^2}.

We know that,

\dfrac{x^a}{x^b}=x^{a-b}

Here, a = 5 and b = 2.

So,

\dfrac{9^5}{9^2}=9^{5-2}\\\\=9^3

So, the answer to the given expression is 9³.

7 0
2 years ago
Other questions:
  • Ron has 8 caps and 4 of his caps are blue. Thes rest of his cap are red. How many of Ron's caps are red
    11·1 answer
  • I need help with this
    7·2 answers
  • a ladder 13m long is placed on the ground in such a way that it touches the top of a vertical wall 12m high. find the distance o
    11·1 answer
  • Lydia had 20 minutes to do a three-problem quiz. She spent 9 7/10
    7·1 answer
  • What’s the units?? Plz need help
    13·1 answer
  • Determine if the triangles are congruent. If yes, by which theorem?
    8·1 answer
  • Suppose we interpret 20÷5 as how much is in each group if there are 5 groups?' Show how you think we could draw a diagram for th
    9·1 answer
  • In a sample of 16 mini-golf balls, 6 are yellow and 10 are pink. If 2 balls are selected at random from the sample, one at a tim
    8·1 answer
  • Please helpp im really bad at math<br> simplify (7v-2)^2
    12·2 answers
  • Solve the following
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!