Find the exact value of the following limit: lim x approaches 0 e^6x... check photo above.
Answers
Substituting x = 0 directly gives the indeterminate form 0/0, so you can use l'Hopital's rule (and you'll have to do that twice):
[tex]\displaystyle\lim_{x\to0}\frac{e^{6x}-6x-1}{x^2}=\lim_{x\to0}\frac{6e^{6x}-6}{2x}=\lim_{x\to0}\frac{36e^{6x}}2[/tex]
The limand is continuous everywhere, so you can plug in x = 0 to get 36•1/2 = 18.
Related Questions
Systems of equations
y=2x+3
y=-x-9
Answers
Answer:
vhguh
Step-by-step explanation:
cfyyghuijofdrr5xtu
Answer:
(-4,-5)
Step-by-step explanation:
[tex]y=2x+3\\y=-x-9=>Multiply(2)=>2y=-2x-18\\\\Add\\3y = -15=>y =-5\\\\Substitute\\x=-y-9=>x=-4[/tex]
12-10 divided by 10+17=
Answers
HI PLEASE HELP ASAP WILL GIVE BRAINLIEST PLEASE HELP THO
Answers
Answer:
105
Step-by-step explanation:
to find the area you would have to do 17 - 7 divided by 2 = 5. so each rectangle is a 7 by 5 so you would do 35 +35+35 = 105.
hope this helps :)
An unknown fraction is between 0 and 1. Which is true about the equivalent percent and decimal?
VI
O The percent and decimal are between 0 and 1.
O The percent and decimal are greater than 1 and less than 100.
O The percent is between 0 and 1, and the decimal is greater than 0 and less than 100.
The percent is greater than 0 and less than 100, and the decimal is between 0 and 1.
Answers
Answer:
The answer is C.
Step-by-step explanation:
The number between 0 and 1. Think of decimals as cents, 100 cents makes a whole. So the number will be greater than 0 but less than 100.
Darius filled up his gas tank with 24 gallons of gas. For each mile that he drives, he uses 0.06 miles of gas. (THE REST OF THE QUESTION IS DOWN BELOW, PLEASE HELP!)
Answers
Answer:
400 miles
Step-by-step explanation:
Step one:
Given data
Darius filled up his gas tank with 24 gallons of gas
Required
The distance 24 gallons will cover
Step two:
1 mile will take 0.06 gallons
hence x miles will take 24 gallons
cross multiply we have
0.06x= 24
divide both sides by 0.06
x= 24/0.06
x=400 miles
Cards numbered 500 through 799 are placed into a box. How many of the cards satisfy both of the conditions shown below?
. The first digit of the three-digit number on the card is odd.
• The three-digit number on the card is divisible by 6.
A
50
33
25
12
Answers
Answer:
33
Step-by-step explanation:
Simplify (4x) ∙ mn ∙ 15 ∙ 2.
Answers
Answer:
(4x)*mn*30
Step-by-step explanation:
Find the whole number that satisfies all of the following conditions.
• It is a whole number between 1 and 100 inclusive.
• 10% of the number is greater than 1 but less than 7.
of the number is a square number.
• The number is not a multiple of 6.
Answers
Answer:
80
Step-by-step explanation:
Please help me with this math problem
Answers
Step-by-step explanation:
according to the question
55x⁶+22x⁴
11x⁴(5x²+2)
so
width:11x⁴
length:5x²+2
omg im so confused someone do number 1 to 5 for me :( this is due in 7 mins. ILL GIVE BRAINLIEST!!
Answers
1.
[tex]a) \: \frac{11}{7} > \frac{10}{9} \\ b) \: \frac{21}{8} > \frac{13}{12} \\ c) \frac{17}{7} < 2 \frac{3}{4} \\ d) \: 1\frac{1}{2} = \frac{24}{16} \\ e) \: \frac{24}{5} = \frac{48}{10} \\ f) \: 3\frac{4}{5} > \frac{78}{25} [/tex]
2.
[tex]a) \frac{9}{4} = \: 2 \frac{1}{4} \\ b) \frac{19}{11} > 1 \frac{1}{6} \\ c) \: \frac{25}{11} < 4\frac{1}{9} \\ d) \frac{41}{3} < 13 \frac{7}{9} \\ e) \: \frac{30}{10} < 3 \frac{1}{2} \\ f) \: \frac{14}{3} > 3 \frac{2}{3} [/tex]
3.
[tex]a) \: \frac{8}{3} ,1 \frac{11}{12} , \frac{7}{4} \\ b) \: \frac{10}{6} ,1 \frac{1}{3} , \frac{8}{8} \\ c) \: \frac{9}{5} , 1\frac{7}{20}, \frac{11}{10} \\ d) \: 2\frac{8}{12} , \frac{13}{6} , \frac{9}{8} [/tex]
4. The first number line, The second number line, The third number line.
5.
[tex]a) \: 3 \frac{30}{60} \: h; \: \frac{210}{60}h \\ b) \: 1 \frac{20}{60} \: h; \: \frac{80}{60}h \\ c) 2 \frac{45}{60} \: h; \: \frac{165}{60}h \\ d) \: 7 \frac{10}{60} \: h; \: \frac{430}{60}h [/tex]
Which equation represents a direct variation?
y = 0.5 x
x minus y = 5
x y = 5
y = x + 5
Answers
Answer:
y+0.5x
Step-by-step explanation:
Just took the test. Got 100%.
Answer:
A. y = 0.5x
Step-by-step explanation:
Simplify this expresion.
(6x^5/2x^2)^2
Answers
Answer:
9x^14
Step-by-step explanation:
PEMDAS
do whats in the parenthesis then do the ^2
Answer:
9x^6
Step-by-step explanation:
1. Cancel the common factor of 6 and 2.
---> (3x^5 / ^2)^2
2. Cancel the common factor of x^5 and x^2.
---> (3x^3)^2
3. Simplify the expression.
---> 9x^6
Divide 3p2 + 6p + 2 by 3p2.
3p? + 6p +2
3p?
30²
+
+
2
3p?
3p? 3p2
= B + C + 2
30
2
Answers
Answer:
Well what is p
Step-by-step explanation:
Answer:
A=6p
B=1
C=2/p
Step-by-step explanation:
Find the greatest possible error for the measurement.
3.5 cm
A.
0.05 cm
B.
0.25 cm
C.
1.75 cm
Answers
Answer:
A. 0.05 cm
Step-by-step explanation:
See your answer below:
You entered the following number: 3.5 cm
The greatest possible error is 0.05 cm
Greatest Possible Error Calculator
Find the measure of each angle indicated.
70°
39°
Answers
Answer:
A. 71
Step-by-step explanation:
70+39= 101
101+71=180
70+39=109
180-109=71 degrees
What is the area of the shaded rectangle
Answers
Answer:
27/70
Step-by-step explanation:
9/10 of the rectangle is shaded on the top and 3/7 of the rectangle is shaded on the side. Multiply those values together to find the area of the shaded rectangle.
9/10 · 3/7 = 27/70
The side lengths of a triangle are 7, 24, and 25. Is this triangle a right triangle?
A) yes
b) no
c) not enough information
Answers
Answer:
yes
Step-by-step explanation:
for it to be a right triangle you should be able to add two of the sides and it be greater than the third side. 7 + 24 > 25
24 + 25 > 7
7 + 25 > 24 therefore it is indeed a right triangle
An elementary school bus comes at 8:15 am every morning to pick up children in a neighborhood. The probability that the bus will be late is 0.19 and the probability that the bus will be early is 0.02.
What is the probability that the bus will arrive early next two days?
What is the probability that the bus will arrive on time next two days?
In two or more complete sentences, explain your calculations for parts A and B. In your explanation, include their similarities and differences.
Answers
Answer:
a. .02 * .02 = .0004
b. (1 - .02 - .19) = .79; .79*.79 = .6241
Step-by-step explanation:
The probability that the bus will arrive on time next two days is 0.79, The probability that the bus will arrive early next two days is 0.0004.
What is Probability?Probability is the likeliness of an event to happen, it has a range from 0 to 1.
Probability that the bus will be late is 0.19
Probability that the bus will be early is 0.02.
The probability that the bus will arrive early next two days is
= 0.02 * 0.02
=0.0004
The probability of coming early one day is small and the probability that it will come early two days in a row is smaller.
The probability that the bus will arrive on time next two days
= (1 - 0.02 -0.19) = 0.79
The probability that the bus will come on time is more as the probability of coming early or late is less.
To know more about Probability
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Leroy borrowed P1500 at an annual simple interest rate of 12%. He paid P270 in interest. For what time period did Leroy borrow the money? A. 8 years B. 5 years C. 18 months D. 18 years
Answers
Answer:
C. 18 months
Step-by-step explanation:
Given data
Principal= P1500
rate= 12%
Simple interest= P270
We know that
Simple interest= PRT/100
substitute
270= 1500*12*T/100
cross multiply we have
270*100= 1500*12*T
27000= 18000 T
divide both sides by 18000
T= 27000/18000
T=1.5 years
That is 12 months + 6 months
in all = 18 months
The time is C. 18 months
A store is offering a $30 mail in rebate on all color printers. Luis is looking at different color printers which range in price from $175 to $425. How much can he expect to spend after the rebate?
Answers
Answer:
145 to 395
Step-by-step explanation:
175 - 30 = 145
425 - 30 = 395
145-395
Which relation is NOT a function?
A
{(a,x),(b,x),(d,z),(c,z)}
B
{(a,y),(b,y),(d,y),(c,y)}
C
{(a,x),(b,y),(a,w),(c,z)}
D
{(a,x),(b,y),(d,x),(c,z)}
Answers
-2x+2y=6
y=3 ft me after ill paypal u 252 622 0255
Answers
Answer:
-2x +6 = 6
-2x = 6- 6
-2x =0
x = 0
Answer:
X= -3+y
Step-by-step explanation:
Nasser is following this recipe to make flapjacks.
Nasser uses 1.8 kg of oats.
How many flapjacks is Nasser making?
Recipe: Makes 10 flapjacks
125 g margarine
120 g sugar
150 ml syrup
225 g oats
40 g sultanas
Answers
1800g / 225g x 10=80
What is the value of the rational expression below when xis equal to 4?
X + 20
X +4
A. 5
O B. 6
O c. 3
O D. 4
Answers
The value of the rational expression when x is equal to 4 is 3.
Option C is the correct answer.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
To find the value of the rational expression (x + 20)/(x + 4) when x is equal to 4,
We substitute 4 for x in the expression:
(4 + 20)/(4 + 4)
= 24/8
= 3
Therefore,
The value of the rational expression when x is equal to 4 is 3.
Learn more about equations here:
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which expression is equivalent to,
2/3x+(-4)(-5)=5x?
A.1-X-91
B. 3x-1
C.1X-93x
D. X + 9
Answers
The coordinate plane shows the outline of a town park. A bike path is to be constructed that runs directly through the park from point E to point G. What will be the length of the bike path to the nearest foot? (1 pt) 20
Answers
Answer:
20
Step-by-step explanation:
that is right...........
Melanie saves $20 every month in her savings account. She withdrew $60 one time to go shopping. She now has $280 in her account. write and solve an equation to determine how many months she has been saving up
Answers
Answer:
20x-60=280
Equation
So x for unknown amount of months, since 20 dollar each month 20x
-60 becuase she withdraws 60 one time
=280 becuase thats what she has left
Now solve
add 60 on both sides
20x=340
Divide 20 on both sides
x=17
17 months
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~ W~h~i~c~h~s~t~a~t~e~m~e~n~t~m~u~s~t~b~e~c~o~r~r~e~c~t~?~
~ Which~statement~must~be~correct?~
~ Which ~ statement ~ must ~ be ~ correct? ~
~Which ~ statement ~ must ~ be ~ correct?~
~Which statement must be correct?~
Which statement must be correct?
Answers
Answer:
Im lost on this one
Step-by-step explanation:
show work please thanks
Answers
Answer:
(6,15)
Step-by-step explanation:
(x,y)
x value is 6(x goes by one)
y value is 15
Determine whether each expression is a polynomial. If it is a polynomial, find the degree and determine whether it is a monomial, binomial, or trinomial.
Answers
The question is incomplete. Here is teh complete question.
Determine whether each expression is a polynomial. If it is a polynomial, find the degree and determine whether it is a monomial, binomail or trinomial.
1. [tex]7ab+6b^{2}-2a^{3}[/tex]
2. [tex]2y-5+3y^{2}[/tex]
3. [tex]3x^{2}[/tex]
4. [tex]\frac{4m}{3p}[/tex]
5. [tex]5m^{2}p^{3}+6[/tex]
6. [tex]5q^{-4}+6q[/tex]
Answer and Step-by-step explanation: The definition of polynomial is "poly" meaning many and Nominal, which means terms. So, Polynomial is an expression of constants, variables, exponents that are combined using mathematical operators: addition, subtraction, multiplication and division.
However, there are exceptions:
Polynomial don't have negative exponent;Polynomial cannot be divided by a variable;Variable cannot be inside a radical;The degree of a polynomial is the highest exponent of that variable. For example for polynomial [tex]3x^5+6x-5x^{2}[/tex] , the degree is 5.
Polynomials have 3 different types:
monomial: only has one term;binomial: has 2 terms;trinomial: has 3 terms;Now, analysing each expression given by the alternatives above:
1. It is a polynomial of degree 3 and trinomial.
2. It is a polynomial of degree 2 and trinomial.
3. Yes, its a polynomial of degree 2 and monomial.
4. It is not a polynomial because it is divided by a variable.
5. A polynomial of degree 5 and it's a binomial.
6. It is not a polynomial due to the exponent being negative.
Answer:
The question is incomplete. Here is the complete question.
Determine whether each expression is a polynomial. If it is a polynomial, find the degree and determine whether it is a monomial, binomial or trinomial.
1.
2.
3.
4.
5.
6.
Answer and Step-by-step explanation: The definition of a polynomial is "poly" meaning many and Nominal, which means terms. So, Polynomial is an expression of constants, variables, exponents that are combined using mathematical operators: addition, subtraction, multiplication, and division.
However, there are exceptions:
Polynomial don't have negative exponent;
Polynomial cannot be divided by a variable;
Variable cannot be inside a radical;
The degree of a polynomial is the highest exponent of that variable. For example for polynomial, the degree is 5.
Polynomials have 3 different types:
monomial: only has one term;
binomial: has 2 terms;
trinomial: has 3 terms;
Now, analyzing each expression given by the alternatives above:
1. It is a polynomial of degree 3 and trinomial.
2. It is a polynomial of degree 2 and trinomial.
3. Yes, it's a polynomial of degree 2 and monomial.
4. It is not a polynomial because it is divided by a variable.
5. A polynomial of degree 5 and it's a binomial.
6. It is not a polynomial due to the exponent being negative.