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
Hatshy [7]
3 years ago
5

Identify the expression with nonnegative limit values. More info on the pic. PLEASE HELP.

Mathematics
1 answer:
marshall27 [118]3 years ago
4 0

Answer:

\lim _{x\to 2}\:\frac{x-2}{x^2-2}\\\\  \lim _{x\to 11}\:\frac{x^2+6x-187}{x^2+3x-154}\\\\ \lim _{x\to \frac{5}{2}}\left\frac{2x^2+x-15}{2x-5}\right

Step-by-step explanation:

a) \lim _{x\to 3}\:\frac{x^2-10x+21}{x^2+4x-21}=\lim \:_{x\to \:3}\:\frac{\left(x-7\right)\left(x-3\right)}{\left(x+7\right)\left(x-3\right)}=\lim \:_{x\to \:3}\:\frac{x-7}{x+7}=\frac{3-7}{3+7}=-\frac{4}{10}=-\frac{2}{5}

b) \lim _{x\to -\frac{3}{2}}\left(\frac{2x^2-5x-12}{2x+3}\right)=\lim \:_{x\to -\frac{3}{2}}\:\frac{\left(2x+3\right)\left(x-4\right)}{\left(2x+3\right)}=\lim \:\:_{x\to \:-\frac{3}{2}}\:\left(x-4\right)=-\frac{3}{2}-4\\ \\ \lim _{x\to -\frac{3}{2}}\left(\frac{2x^2-5x-12}{2x+3}\right)=-\frac{11}{2}

c) \lim _{x\to 2}\:\frac{x-2}{x^2-2}=\frac{2-2}{\left(2\right)^2-2}=\frac{0}{4-2}=0

d) \lim _{x\to 11}\:\frac{x^2+6x-187}{x^2+3x-154}=\lim _{x\to 11}\:\frac{\left(x-11\right)\left(x+17\right)}{\left(x-11\right)\left(x+14\right)}=\lim _{x\to 11}\:\frac{\left(x+17\right)}{\left(x+14\right)}=\frac{11+17}{11+14}=\frac{28}{25}

e) \lim _{x\to 3}\:\frac{x^2-8x+15}{x-3}=\lim \:_{x\to \:3}\:\frac{\left(x-3\right)\left(x-5\right)}{x-3}=\lim _{x\to 3}\left(x-5\right)=3-5=-2

f) \lim _{x\to \frac{5}{2}}\left(\frac{2x^2+x-15}{2x-5}\right)=\lim \:_{x\to \:\frac{5}{2}}\frac{\left(2x-5\right)\left(x+3\right)}{2x-5}=\lim \:\:_{x\to \:\:\frac{5}{2}}\left(x+3\right)=\frac{5}{2}+3=\frac{11}{2}

You might be interested in
Please help and show work
sashaice [31]
The answer to the question is 14

x^4 + 14x^2 + 49


(x^2 + 7)^2

perfect square
3 0
3 years ago
lia gets paid $450 a week pluse commission on het sale. she hopes to earn at least $600 each week. write an inequality to repres
FrozenT [24]
So commission will be $150 450+_=600
3 0
3 years ago
What is the answer to 5^-16+24 with solution​
wariber [46]

Answer:

24

Step-by-step explanation:

i used calculator. it is so easy

3 0
2 years ago
PLZZZ HELP ME 10 PTSS
Anestetic [448]

Answer:

5 31/ 30 or 6 1/30

Step-by-step explanation:

I wish this helped you

5 0
3 years ago
Read 2 more answers
Please help asap will mark brainliest!!!!
Lady_Fox [76]

Answer:

2,600.00

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • How do you multiply 40 7 /16?
    11·2 answers
  • How to convert 1500 ml to liters
    14·1 answer
  • A parallelogram has symmetry with respect to the line that _____.
    12·2 answers
  • Which equation represents a line which is parallel to the line y=4x-8y=4x−8?
    11·1 answer
  • If i was born in 1996 how old am i in 2017
    12·2 answers
  • The function f(x) = (x - 4)(x - 2) is shown.
    7·1 answer
  • Suppose Aldo borrows $5500 at an interest rate of 9% compounded each year assume that no payments are made on the loan how much
    5·1 answer
  • Roman is born in the year 123 BC and dies at the age of 74 years. Use a negative number to express the year in which he dies
    8·1 answer
  • Help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
    12·2 answers
  • If the digit in ones place of a number is 3 .Then the last digit of its cube will be
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!