: Discuss the continuity of the function f(x)=xtan(1/x) at x = 0 given that x≠0 and f(0)=0.
Answer:
Left hand Limit = Right Hand Limit = f(a)
it is a continuous function.
Step-by-step explanation:
Solution:
In order to find out the continuity of the function, we need to keep in mind following things:
Left hand Limit = Right Hand Limit = f(a)
Where, f(x) = exists and f(a) = defined.
Data Given:
f(x) = x tan(1/x) x [tex]\neq[/tex] 0 (this function is used when x > 0 and x<0)
f(x) = 0 when x = 0
First we have to check the Left hand Limit.
L.H.L = f(0-h) (x<0)
Lim[tex]_{x-->0^{-} }[/tex] f(x)
Lim[tex]_{x-->0^{-} }[/tex] x tan (1/x)
Put x = 0-h
Lim[tex]_{x-->0^{-} }[/tex] (0-h) tan (1/(0-h))
Lim[tex]_{x-->0^{-} }[/tex] h tan (1/h)
Putting h = 0
(0) x (tan(1/0)))
As we know, for tanx value is a finitely oscillatory between -∞ to +∞
Hence, 0 x finite number then,
L.H.L = 0
Similarly,
R.H.L = f(0+h)
Lim[tex]_{x-->0^{+} }[/tex] (0+h) tan (1/(0+h))
Lim[tex]_{x-->0^{+} }[/tex] (h) tan (1/(h))
R.H.L = 0
Now, as we know, when x = 0
f(x) = 0
f(0) = 0
Left hand Limit = Right Hand Limit = f(a)
Hence, it is a continuous function.
Devi rides the bus to her grandmother's house every day. She tracked how many minutes the bus rides took for one week: 24 32 25 24 30 30 24 calculate the mean, median, range, and mid range of the bus ride times for a week
Answer:
Mean: 27
Median: 25
Range: 8
Mid Range: 28
Step-by-step explanation:
The value of mean, median, range and mid range will be 27 , 24 , 8 and 28 respectively.
It is given that the time in minutes for which Devi rides the bus in a week is 24, 32, 25, 24, 30, 30, 24.
We have to find out the value of mean, median, range and mid range.
What is mean of numbers ?
The mean of numbers is the ratio of sum of all numbers to the total no. of numbers.
As per the question ;
The time in minutes for which Devi rides the bus in a week is ;
24, 32, 25, 24, 30, 30, 24.
So ;
The mean will be ;
= [tex]\frac{24 + 32 + 25 + 24 + 30 + 30 +24}{7}[/tex]
= [tex]\frac{189}{7}[/tex]
= 27
and
We know that when n is odd number then ; Median is ;
= [tex]\frac{n+1}{2}th[/tex] term
= [tex]\frac{8}{2}th[/tex] term
= 4th term
= 24
and
Range will be ;
= largest number - smallest number
= 32 - 24
= 8
and
Mid range will be ;
= (largest number + smallest number) / 2
= [tex]\frac{32 + 24}{2}[/tex]
= 56 / 2
= 28
Thus , the value of mean, median, range and mid range will be 27 , 24 , 8 and 28 respectively.
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Help I’m being timed!!
Answer:
Area of circular trail = 7.1 square miles
Step-by-step explanation:
Given that:
Distance covered by Mr. Baker = 6 miles
As this distance is of both sides, we will divide it by 2 which will give us the diameter of the circle.
Distance of one side = 6/2 = 3 miles
Diameter = 3 miles
Radius = 3/2 = 1.5 miles
Area of circle = [tex]\pi r^2[/tex]
Area of circle = [tex]3.14*(1.5)^2[/tex] = 3.14 * 2.25
Area of circle = 7.065 = 7.1 square miles
Hence,
Area of circular trail = 7.1 square miles
Raul wants to buy a new collar for each of his 5 dogs. The collars come in a choice of 10 different colors. Step 1 of 2 : How many selections of collars for the 5 dogs are possible if repetitions of colors are allowed
Answer:
100,000
Step-by-step explanation:
Calculation for How many selections of collars for the 5 dogs are possible if repetitions of colors are allowed
Based on the information given since he has 5 dogs that he want to purchase a collar for, which means that if the collar has 10 choice of variety of colors, then the selection of collars for the 5 dogs if repetitions of colors are allowed will be calculated as:
Selections of collars=10*10*10*10*10
Selections of collars=100,000
Therefore the numbers of selections of collars for the 5 dogs that are possible if repetitions of colors are allowed is 100,000
What is 147.5% as a decimal?
Answer:
1.475
Step-by-step explanation:
When we have a percentage and want to convert it to the decimal, we want to move the decimal 2 places to the left (away from the percentage) or divide by 100.
147.5/100 = 1.475
show equation has a slope of -3 and a y-intercept of 8
Answer:
y=-3x+8
Step-by-step explanation:
The supreme choice pizza at Maria's Pizza Palace contains 2 different meats and 4 different vegetables. The customer can select any one of 5 types of crust. If there are 4 meats and 7 vegetables to choose from, how many different supreme choice pizzas can be made
Answer: Number of different supreme choice pizzas that can be made is 1050
Step-by-step explanation:
Given the data in the question;
Number of ways in which crust can be selected = 5
Number of ways in which 2 meats can be selected from 4 = ⁴C₂
⇒ 4! / ( 2! x (4-2)! )
= 6
Number of ways in which 4 vegetables can be selected from 7 = ⁷C₄
⇒ 7! / ( 4! x (7-4)! )
= 35
so; Number of different supreme choice pizzas that can be made;
⇒ 5 × 6 × 35
= 1050
Therefore, Number of different supreme choice pizzas that can be made is 1050
What is the result of adding these two equations?
- 2x + y = -5
- 2x - 4y = 6
Answer: 5y = -11
Step-by-step explanation:
-2x + y = -5
(-2x - 4y = 6) -1
-2x + y = -5
2x + 4y = -6
System by elimination method
0 + 5y = -11
5y = -11
Answer:
-4x-3y=1
Step-by-step explanation:
when adding the wo equations, u must add like ters. -2x+-2x is -4x. and positive y+ -y= -3y and-5+6=1. so if u put it all together after adding all integers you get -4x-3y=1
(9g+7)+(3g+6) what is the awnser simplify
Answer:
12g+13 can I have brain lest...
Answer:
12g+13
Step-by-step explanation:
(9g+7)+(3g+6) (rewrite and remove the parentheses)
9g+7+3g+6 (collect the like terms and calculate)
solution: 12g+13
hope this helps!
1. Enter the linear inequality shown in the graph.
Answer:
y=1/3x+2
Step-by-step explanation:
Find two points and find the x and y distance between them to get the slope. I did (0,2) and (6,0), and the distance between them was 2/6 which simplifies into 1/3.
Then (0,2) is the y-intercept because it's where the line crosses the y-intercept.
(hope this helps :P)
f(2) =______________
Answer:
(2,-2)
Step-by-step explanation:
the graph...
You are taking a test in math. There are 20 questions and 30 minutes.
How many questions do you have for 12 minutes?
______questions
How much time do you have for 15 questions?
_________minutes
How much time do you have for 5 questions?
________minutes
Answer:
8, 10, 3.3333
Step-by-step explanation:
look at the picture for an explanation,
use the same method for all 3
If Steph Curry can shoot 72 free throws in 12 minutes, how many free throws
would he shoot each minute?
Answer:
6
Step-by-step explanation:
72/12=6 shoots each minute
Answer:
The answer is 6
Step-by-step explanation:
72 divided by 12 = 6
Determine whether the given statement is true or false.
13 € {1, 2, 3,..., 23}
Choose the correct answer below.
O True
False
Answer:
true, because 13 is belong to 1 to 23 between number so,
HELP ME PLEASEEEEEEEEE
Answer:
3r
Step-by-step explanation:
there is an invisible 1 in front of the rs. Add them and you get 3r
Answer:
3r
Step-by-step explanation:
Let's replace r with a number.
For example,
r=3
3+3+3=9
We know also that 9=3 multiplied by 3. Therefore, r+r+r=3r
PLZ I NEED ANSWERS. THIS IS MIDDLE SCHOOL LEVEL NOT COLLEGE
WILL DO ABSOLUTELY ANYTHING FOR THIS ONE HELP ASAP TIMES
9514 1404 393
Answer:
A) -1 < x < 0
Step-by-step explanation:
The horizontal line that is the x-axis is also the line y = 0. The curve is above that line when x < 0, and when x > 3.6.
The only interval that overlaps either of these regions is ...
(A) -1 < x < 0
pls help asap !!!!!!
Answer:
could you try 33?
Step-by-step explanation:
if Rs is half that could be qt and z is the other 33.
A scuba diver was at a depth of −8012 feet. How many feet did the scuba diver ascend if the diver traveled to the surface of the ocean?
The scuba driver traveled to the sea level which is 8012 feet
what is sea level?Sea level is measured in relation to the adjacent land. Just like the ocean, the elevation of land may rise and fall over time. For example, the tremendous weight of a glacier on land pushes the land down, closer to sea level. And the sea level at the surface of the ocean is considered to be zero.
Given here, he dived to a depth -8012 feet so he has to ascend again by + 8012 feet to reach the surface of the ocean .
Hence, he traveled 8012 feet.
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who ever anwser my question fast and is quick i will give any body 200 point i will any one
Answer:
omg, can i have freeee points?? :,)
Step-by-step explanation:
Answer: Sure, but I want to be the brainiest for extra points :)
Step-by-step explanation:
8936245x18463 brainlist to who gets this right
Please answer this question (image attatched
..................Is this a joke?
The pyramid has a base that is a right
triangle with side lengths 3 feet , 4 feef , 5 feet .it’s height is 6 feet. What is the volume of the pyramid?
Answer:
36
OR
12
?
Step-by-step explanation:
Area of Triangle: [tex]\frac{3*4}{2} = 6[/tex]
Volume: 6*6 = 36
Pyramid part confuses me.
volume of a pyramid: [tex]\frac{1}{3}*B*H[/tex] = [tex]\frac{1}{3}*6*6[/tex] = 12
B = triangle area
H = height
Keshon's mother drives Keshon to his grandmother's house to visit. First she drives 60 minutes at a constant speed of 40 mph. Then they reach the highway. She speeds up and drives for another 30 minutes at a constant speed of 70 miles mph
1) How long did the trip take?
2) How far did Keshon and his mother drive together?
Answer:
60+40+30+70=200 this an answer of a and B is 200
Answer:
A. 60+40+30+70=200
B. 200
Step-by-step explanation:
Hope this helps have an amazing day/month/year!
If 2.29 x 19.79 = 45.3191, then without actual multiplication the value of 0.0229 x 1979 is?
If you answer this first, I will give brainliest.
Answer:
45.3191
Step-by-step explanation:
0.0229 is 100 times smaller that 2.29 but 1979 is 100 times greater than 19.79. Since they cancel each other out, the answer remains the same.
5 m
9 m
18 m
24 m
10 m
9 m
What is the volume of the figure? Enter the answer in the box.
Answer:
where is figure by the way
A six-month $3600 treasury bill sold for $3411. What was the simple annual discount rate?
Answer:
0.9235%/month
Step by step explanation:
r = (1/6)((3600/3411) - 1) = 0.00923483
r = 0.00923483
Converting r decimal to R a percentage
R = 0.00923483 * 100 = 0.9235%/month
Answer:
one hundred eighty-nine dollars
Write the phrase as an expression.
28 divided by 7
An expression is ____.
Answer: 28/7
Step-by-step explanation:
Answer:
28/7=4
Step-by-step explanation:
nnei
Please help asap
During a sale at a department store, all ties are discounted by 75%. A customer buys a tie that was originally priced at $135. If an 8% sales tax was added after the discount was
taken, about how much money does the customer have to pay?
O $109.35
O $60.75
O $36.45
O $33.75
O $68.00
Answer:
answer of this qn is 36.45
Step-by-step explanation:
135×108÷100 then 145.8 will come and then 145.8×25÷100 hence ans will 36.45
What is the slope of the line that passes through the points (1,1) and (-1,5)