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
hammer [34]
3 years ago
12

Lim x--> 0 (e^x(sinx)(tax))/x^2

Mathematics
1 answer:
Tom [10]3 years ago
4 0

Make use of the known limit,

\displaystyle\lim_{x\to0}\frac{\sin x}x=1

We have

\displaystyle\lim_{x\to0}\frac{e^x\sin x\tan x}{x^2}=\left(\lim_{x\to0}\frac{e^x}{\cos x}\right)\left(\lim_{x\to0}\frac{\sin^2x}{x^2}\right)

since \tan x=\dfrac{\sin x}{\cos x}, and the limit of a product is the same as the product of limits.

\dfrac{e^x}{\cos x} is continuous at x=0, and \dfrac{e^0}{\cos 0}=1. The remaining limit is also 1, since

\displaystyle\lim_{x\to0}\frac{\sin^2x}{x^2}=\left(\lim_{x\to0}\frac{\sin x}x\right)^2=1^2=1

so the overall limit is 1.

You might be interested in
What does 17/10x 10/17 equal
Rasek [7]
\frac{17}{10}\times\frac{10}{17}=\frac{17\times10}{10\times17}=\frac{170}{170}=1

5 0
1 year ago
Jill is factoring the expression 13XY -52y. Her work is shown below
Sunny_sXe [5.5K]

Answer:13y(x-4)

Step-by-step explanation:

13xy-52y =13y(x-4)

3 0
3 years ago
Which of the following is a trinomial with a constant term?
Leto [7]
I think the answer is b
4 0
3 years ago
As of right now, Katie’s college fund has $601.85. If she deposits a check for $225, how much money will she have in her college
sashaice [31]
I’m pretty sure it’s $826.85 because deposit means to put money into something. So, you’d just add $601.85 to $225 to get your answer. I think.
4 0
3 years ago
There are 60 people waiting in line for a movie. If 20 percent are wearing hats, how many people in line were not wearing hats?
sammy [17]

Answer:

48 people

Step-by-step explanation:

To find 20% of 60, you multiply 60 by .2 and get 12. Subtract 12 from 60, and 48 people were not wearing hats.

4 0
3 years ago
Other questions:
  • The graph shows the solution to which system of equations?
    6·1 answer
  • A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associ
    12·1 answer
  • Simplify....................
    9·1 answer
  • The minute hand of a clock is 5 cm long. What is the linear velocity, in centimeters per minute, at the tip of the minute hand?
    6·2 answers
  • What property is (3×4) 5 =(5×4) 3
    12·2 answers
  • The highest temperature recorded in the town of
    15·1 answer
  • Green apples cost $1.89 per pound. Alice purchased 3 ½ pounds of apples. How much did she pay?
    14·1 answer
  • 5
    13·1 answer
  • Rachel types 50 words per minute. She needs to type a 1,500 word report. Determine how many minutes it will take her to type the
    12·2 answers
  • (Score for Question 1: of 4 points)
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!