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
Nataly_w [17]
2 years ago
15

lim x rightarrow 0 1 - cos ( x2 ) / 1 - cosx The limit has to be evaluated without using l'Hospital'sRule.

Mathematics
1 answer:
zaharov [31]2 years ago
6 0

Answer with Step-by-step explanation:

Given

f(x)=\frac{1-cos(2x)}{1-cos(x)}\\\\\lim_{x \rightarrow 0}f(x)=\lim_{x\rightarrow 0}(\frac{1-(cos^2{x}-sin^2{x})}{1-cos(x)})\\\\(\because cos(2x)=cos^2x-sin^2x)\\\\\lim_{x \rightarrow 0}f(x)=\lim_{x\rightarrow 0}(\frac{1-cos^2x}{1-cos(x)}+\frac{sin^2x}{1-cosx})\\\\=\lim_{x\rightarrow 0}(\frac{(1-cosx)(1+cosx)}{1-cosx}+\frac{sin^2x}{1-cosx})\\\\=\lim_{x\rightarrow 0}((1+cosx)+\frac{sin^2x}{1-cosx})\\\\\therefore \lim_{x \rightarrow 0}f(x)=1

You might be interested in
What is fo)?<br> O O only<br> 0 -6 only<br> 0-2, 1, 1, and 3 only<br> 0 -6, -2, 1, 1, and 3 only
mash [69]

Answer:

  -6 only

Step-by-step explanation:

f(0) is the value of y when x=0. This is the graph of a 4th-degree polynomial, so is a function. There is only one y-value for x=0. That is where the graph crosses the y-axis, at y = -6.

  f(0) = -6 . . . . only

8 0
3 years ago
one fabric costs $15.00 for two yards. Another costs $37.50 for 5 yards. Do these fabrics have the same unit cost? explain
kondaur [170]
Yes they do becuase
$15 divided by 2 equals $7.50
Then you do 5 times $7.50 and your anwser is $37.50
They total unit cost for each is $7.50
6 0
2 years ago
Two trains leave a city at 3 P.M. One train goes east at a constant rate of 70 mph. The other goes west at a rate of 62 mph. How
andrey2020 [161]

Answer:

4 hours

Step-by-step explanation:

The general formula for distance, rate and time is:

d = rt, where distance is the product of rate multiplied by time

Given that one train is moving at a rate of 70 mph and one is moving at a rate of 62 mph in the opposite direction, the combined distance over time is equal to 528 miles.  Using the variable 't' for time:

70t + 62t = 528

Combine like terms: 132t = 528

Divide both sides by 132: 132t/132 = 528/132  or t = 4 hours

8 0
3 years ago
Read 2 more answers
Which is larger, 7/10 or 3/4?
DIA [1.3K]
3/4 is larger than 7/10.
3 0
3 years ago
Read 2 more answers
Some please help it urgent
Phoenix [80]

Answer: y axis = 20 x axis = 430

Step-by-step explanation: YOU´RE STUPID

8 0
2 years ago
Other questions:
  • Hal forgot the number of people at the basketball game he does remember that the number had four digits and three in the tens pl
    7·1 answer
  • Flora’s car is 59/100 meters longer than Sally’s car.Sally’s car is 2/10 of a meter longer then Trevor’s car.how many longer is
    14·1 answer
  • Which statement is true of the function f(x) = -3x? Select three options.
    10·1 answer
  • I CANT FIGURE OUT HELP ME!!! SOLVE FOR W: −(14w+8)+8=3<br><br>IM GIVING MAX POINTS I CAN!!!!!
    9·2 answers
  • How many roots does the polynomial function, y=(x-8)(x+3)^2 have?
    11·2 answers
  • The sum of five times a number and -6 is -2.
    14·1 answer
  • 7h + 3 = 7(2+h) -11 <br> this is my question
    5·1 answer
  • 2 __ a solution of 4 = k/4<br><br> is it or is it not
    10·2 answers
  • (QUICK I NEED HELP)
    13·2 answers
  • I cant figure out this project to save my life anyone able to help me?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!