Answers
Answer: [tex]\frac{-m^2+n^2}{2}[/tex]
If the font is too small, it says (-m^2+n^2)/2
==============================================
Explanation:
If you plug x = 0 into the original expression, then you'll get the indeterminant form 0/0 after simplifying.
Recall that cos(0) = 1
So we use L'Hospitals rule to derive the numerator and denominator separately (don't use the quotient rule)
[tex]\displaystyle \lim_{x\to0} \frac{\cos(mx)-\cos(nx)}{x^2}\\\\\\\displaystyle \lim_{x\to0} \frac{-m\sin(mx)+n\sin(nx)}{2x}\\\\\\[/tex]
Plug x = 0 into this new expression. You should get 0/0 again here as well, which means you'll have to do another round of L'Hospital
[tex]\displaystyle \lim_{x\to0} \frac{-m^2\cos(mx)+n^2\cos(nx)}{2}\\\\\\[/tex]
Now plugging in x = 0 leads to something that isn't indeterminant
Evaluating the limit gets us
[tex]\displaystyle \lim_{x\to0} \frac{-m^2\cos(mx)+n^2\cos(nx)}{2}\\\\\\=\frac{-m^2\cos(m*0)+n^2\cos(n*0)}{2}\\\\\\= \frac{-m^2+n^2}{2}\\\\\\[/tex]
Related Questions
John 3 miles on Monday, 2 miles on Tuesday. He ran 4 more miles on Wednesday then he did on Monday. How many miles did John run Monday through Wednesday?
Answers
Answer: John ran 10 miles through Monday and Wednesday.
Step-by-step explanation: He ran for miles on 4 but 4 more than Monday and he ran 3 miles on Monday, so you add 4 + 3 which = 7 then you add 3 to 7 because he ran 3 miles on Monday then you get 10.
Please help this is Math
Answers
Answer:
I cant see the reference image so I dont have enough info to help. Srry :(
Step-by-step explanation:
36/40 to lowest term
Answers
Answer:
9/10
Step-by-step explanation:
36/4=9
40/4=10
Twice a number, decreased by 58 is less than 112
Answers
Answer:
2x-58<112
Step-by-step explanation:
Please look at the image.
Answers
Answer: C or 6/5
Step-by-step explanation: the question is 4/5 plus 2/5 so 6/5
Test Prep There are 80 marbles in a bag. If 30% of the marbles are green, how many marbles are not green
Answers
Hey there!
Step 1: Calculate percentage
Since 30% of the marbles are green
=> 80 × 30/100
=> 8 × 30/10
=> 240/10
=> 24
So, 24 of the marbles are green
Step 2: Substract 24 from 80
=> 80 - 24
=> 56
Therefore, 56 marbles are not green
At 12:00 AM (hour 0 of the day) the tide at a certain beach was at its lowest level of the day: 1.0 feet. At 6:00PM (hour 18 of the day) the tide at a certain beach was at its highest level of the day: 2.0 feet. Assuming that this tide follows a sinusoidal model, about how high would you expect the tide to be at noon?
Answers
Answer:
At noon the tide will be at the lowest point which is 1 ftStep-by-step explanation:
please see attached a sketch of the solution for your reference
What is a sinusoidal wave?
Alternatively called a sine wave is a type of wave that shows a repetitive pattern or oscillation, it normally starts from a low point moves to the next point which is usually higher than the previous and repeats itself as the whole process continues
How can you determine the difference between square root and cube functions?
Answers
Solve the inequality. And show work please
5
-- y = 12
6
Answers
Answer:
y= [tex]\frac{72}{5}[/tex] or 14.4
Step-by-step explanation:
[tex]\frac{5}{6}y = 12\\[/tex]
Multiply both sides by 6/5, the reciprocal of 5/6.
[tex]y = 12 * (\frac{6}{5} )[/tex]
Express 12 x (6/5) as a single fraction.
[tex]y = \frac{12 * 6}{5}[/tex]
Multiply 12 and 6 to get 72.
[tex]y = \frac{72}{5}[/tex]
Step by step:
1) x6 on both sides = 5y=72
2)divide both sides by 5= y=14.4
If you place a 37 ft ladder against the top of a 12 ft building how many ft will the bottom of the ladder be from the bottom of the the building
Answers
Answer: 25 feet
Step-by-step explanation:
If you place a 37 foot ladder against the top of a 12 food building, since 37 is greater than 12 the ladder will keep going past the building.
37-12=25
the ladder will be 25 feet from the bottom of the building
hope this helped :)
A dilation has center (0,0). Find the image of the point A(-5,5) for the scale factor 1.2.
Answers
Step-by-step explanation:
Since the dilation is centered at the origin, you can multiply each of the coordinates by the scale factor. This means the image is A'(-6, -6)
Select all of the names that apply to -24
Answers
Answer:
I need an image to help you.
Step-by-step explanation:
Answer:
Integer, rational number, and real number
Step-by-step explanation:
Integer is a number that can be either positive or negative, but can't be a fraction or irrational number such as pi. It's also a subset of rational numbers, which is a subset of real numbers.
brainiest to who ever answers first
Answers
Answer:
18/24 for the first one
Step-by-step explanation:
please help me with both of these
Answers
Answer:
1. Square is a box shape so you can tell her it can be shaped like an package
2.Tell Alex any real numbers a and b, if ab = 0, then that means a equals zero, or b equals zero, but sometimes both a and b equal zero
Step-by-step explanation:
I hope this helps!
IMHO I think Alex will be really confused
three green socks, four red socks, and five blue socks are in a drawer, and 2 socks are withdrawn at random. Find the probability of one blue sock and one red sock
Answers
Step-by-step explanation:
Number of socks: 3+4+5= 12
Number of red socks= 4
Red socks/other socks= 4/12
Simplify: fraction: 1/3
percentage: 33.33%
decimal: 0.3333
A , B and C form a triangle where ∠ B A C = 90 ∘ . A B = 0.5 mm and B C = 15.4 mm. Find the length of A C , giving your answer rounded to 1 decimal place.
Answers
Answer:
15•4 mm
Step-by-step explanation:
using sine rule
a÷ sinA=c ÷sinC
15•4÷sin90=0•5÷sinC
sinC =0•5 × sin90 ÷ 15•4
C =1•9°
A+B+C= 180
90+B+1•9=180
B= 88•2°
b÷sinB = a÷sinA
b÷sin88•2= 15•4÷sin90
b=sin88•2 ×15•4 ÷sin90
b =15•39
to 1 dp
b =15•4 mm
Hi, so I think I got this right but do you have to put a negative symbol anywhere or just leave it how it is? number 12 (sorry is blurry my back camera is broken)
Answers
Answer:
Just leave it how it is, you don't have to do anything with the negative symbol.
Could I please have BRAINLIEST?Please help on this practice paper my parents couldn’t solve this either
Answers
We are given that ,
[tex]{:\implies \quad \sf \dfrac{12+\sqrt{128}}{1-\sqrt{2}}=a+b\sqrt{2}}[/tex]
Consider LHS;
[tex]{:\implies \quad \sf \dfrac{12+\sqrt{128}}{1-\sqrt{2}}}[/tex]
Can be further written as ;
[tex]{:\implies \quad \sf \dfrac{12+8\sqrt{2}}{1-\sqrt{2}}}[/tex]
Rationalizing the denominator we have ;
[tex]{:\implies \quad \sf \dfrac{12+8\sqrt{2}}{1-\sqrt{2}}\times \dfrac{1+\sqrt{2}}{1+\sqrt{2}}}[/tex]
[tex]{:\implies \quad \sf \dfrac{(12+8\sqrt{2})(1+\sqrt{2})}{(1-\sqrt{2})(1+\sqrt{2})}}[/tex]
[tex]{:\implies \quad \sf \dfrac{12(1+\sqrt{2})+8\sqrt{2}(1+\sqrt{2})}{1-2}}[/tex]
[tex]{:\implies \quad \sf \dfrac{12+12\sqrt{2}+8\sqrt{2}+16}{-1}}[/tex]
[tex]{:\implies \quad \sf \dfrac{28+20\sqrt{2}}{-1}}[/tex]
[tex]{:\implies \quad \sf -28-20\sqrt{2}}[/tex]
Hence, we can conclude that ;
[tex]{\bf a=-28}[/tex] [tex]{\bf b=-20}[/tex]IM IN A BIG BIG RUSH HELP PLEASE
Answers
Answer:
Perimeter = 10
Step-by-step explanation:
Horizontally 3 units; vertically 2 units.
If h is horizontal measure, and v is vertical measure, then perimeter is 2(h+v) and area is hv.
[4] The Perimeter of the rectangle is how many units?
Perimeter formula ; 2(h+v)
2(3+2) = 10
~Learn with Lenvy~
HELP PLEASE! 40 POINTS AND WILL MARK BRAINLIEST.
The number 97 is a term of the sequence defined by the explicit rule f(n)=4n-3. Which term in the sequence in 97? Justify your answer.
Answers
Answer:
The 25th term is 97
Step-by-step explanation:
The explicit rule is f(n)=4n-3
Let f(n) = 97
97 = 4n-3
Add 3 to each side
97+3 = 4n-3+3
100 = 4n
Divide by 4
100/4 = 4n/4
25 = n
A car travels at a constant speed, as shown on the double number line. How far does the car travel in 14 hours?
Time (hours) 1 2 3
Distance (kilometers) 70 140 210 (for 3)
How far does the car travel in 14 hours? Explain or show your reasoning
Answers
Answer:
980km
Step-by-step explanation:
Multiply 14 by 70
Kofi sliced a watermelon into 9 equal parts .If each part had 87 seeds,how many seeds did each watermelon have?
Answers
The watermelon has 783 seeds
Answer:
783 seeds in each watermelon
Step-by-step explanation:
bc if each watermelon has 87 seeds u just multiply
What is the period of the function f(x) shown in the graph?
Answers
Answer:
[tex]\dfrac{\pi }{2}[/tex]
Step-by-step explanation:
The period of the function is from one peak to the next (or from one trough to the next).
[tex]\sf \implies period=\dfrac{\pi }{2}[/tex]
**see attached for the measurement of the period for this function**
ABCD is a parallelogram. Find z.
Answers
Step-by-step explanation:
here is the answer Step-by-step for you
I hope you understand...
if you brought 20 stamps for 0.45 each and 15 stamps for 0.32 each how much money did you spend on stamps
Answers
Answer:
$13.8
Step-by-step explanation:
20(0.45)+15(0.32)
= 13.8
PLEASE HELP The hourly wage of some Toyota automobile assembly line workers is being increased annually by the same percentage
If their wage went from $6.80 to $10.19 in 7 years what is the doubling time?
Answers
Answer:
1928374.193 %
thats my answer
Which equation represents a line that passes through (-2,4) and has a slope of 2/5?
Answers
Answer:
A
Step-by-step explanation:
The slope is 2/5. Plug in the points and slope into the slope- intercept form y-y1=m(x-x1).
It would be...
y-4=2/5(x+2)
Which statement best explains the value of 12-(-4)??
Answers
Answer:
16................
Step-by-step explanation:
Above
Answer:
The answer is 16.
Step-by-step explanation:
Negatives can be tricky, but once you get the hang of it, it will be much easier! The rule to remember here is:
"Anything 'minus a negative' just means plus, because the negatives cancel each other out."
a. For example, 4 -(-1) is the same thing as 4+1, which equals 5.
b. In this problem, 12-(-4) is the same thing as 12+4, which equals 16.
I hope this helps! Feel free to give me Brainliest if you feel this helped. :)
double u, divide v by the result, then add t to what you have
Answers
do u want me to solve it to??
Please help me with find the slope
Answers
Answer: Finding the slope
Step-by-step explanation:
I'm sorry but the pic is a but blurry so basically you pick two points and use the equation 2y-y1/2x-1x then simplify if you can find a better picture I would love to help.
Answer my question please on my page :)