Mathematics College

(1+h): - 1
A. lim
h>0
h
f(0) =
х
a =
1
B. lim
h>0
cos(1 + h) +1
h
f(3) =
a =
7T
5(4+ h)" - 5120
C. lim
h->0
h
f(x) =
a =
4
o
D. lim
h 0
e4h - 1
h
f(x) =
a =
e
Х
Pls take a look at the picture

(1+h): - 1A. Limh>0hf(0) =a =1B. Limh>0cos(1 + H) +1hf(3) =a =7T5(4+ H)" - 5120C. Limh->0hf(x)

Answers

Answer 1

Each of these limits correspond to the derivative of some function f(x) at a point x = a.

Recall the limit definition of a function f(x) :

f '(x) = lim [h → 0] ( f(x + h) - f(x) ) / h

Then if x = a, we get

f '(a) = lim [h → 0] ( f(a + h) - f(a) ) / h

From here, it's easy to identify what each function and point should be:

(a) f (a + h) = (1 + h)¹ʹ³   →   f(x) = x ¹ʹ³ and a = 1

(that's a 1/3 in the exponent)

(b) f (a + h) = cos(π + h)   →   f(x) = cos(x) and a = π

(c) f (a + h) = 5 (4 + h)⁵   →   f(x) = 5x ⁵ and a = 4

(d) f (a + h) = exp(4h) = exp(4 (0 + h))   →   f(x) = exp(4x) and a = 0

(where exp(x) = eˣ )

Related Questions

A little help with this math problem

Answers

Answer:

The length of the last side is 9 metres

Step-by-step explanation:

Solve for "T" in the following formula: P= NRT/V

Answers

Answer:

T = PV / NR

Step-by-step explanation:

Mariah Jacobsen is the marketing manager at ABC Electronics, a major consumer electronics supplier in the northwest. Over the last five years, sales of the company's flagship product - the Wizer Anonymizer (the WA) - have been 45000, 45500, 44500, 46000 and 44000 units. This rate of sales is considered average for the product over the last twenty years or so. Ms. Jacobsen believes that the distribution of the WA's sales is normal with a standard deviation of 1500 units. If she were asked to make a forecast of next year's sales to upper management, what is the likelihood that she would be correct if she predicts sales between 43000 and 46000?

Answers

Answer:

0.6568 = 65.68% probability that she would be correct.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

45000, 45500, 44500, 46000 and 44000 units. This rate of sales is considered average for the product over the last twenty years or so.

This means that:

[tex]\mu = \frac{45000 + 45500 + 44500 + 46000 + 44000}{5} = 45000[/tex]

Standard deviation of 1500 units.

This means that [tex]\sigma = 1500[/tex]

What is the likelihood that she would be correct if she predicts sales between 43000 and 46000?

This is the pvalue of Z when X = 46000 subtracted by the pvalue of Z when X = 43000. So

X = 46000

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{46000 - 45000}{1500}[/tex]

[tex]Z = 0.67[/tex]

[tex]Z = 0.67[/tex] has a pvalue of 0.7486

X = 43000

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{43000 - 45000}{1500}[/tex]

[tex]Z = -1.33[/tex]

[tex]Z = -1.33[/tex] has a pvalue of 0.0918

0.7486 - 0.0918 = 0.6568

0.6568 = 65.68% probability that she would be correct.

A wire is attached to the top of a tower and to a point on the ground that is 35 m from the base of the tower. If the wire makes a 65 degree angle with the ground, how long is the wire? Round your answer to the nearest tenth

Answers

Answer:

83 m

Step-by-step explanation:

The computation of the length of the wire is shown below:

Let us assume the length of the wire be x

Given that

There is 35m from the base of the tower

And, the angle with the ground is 65 degree

So, the length of the wire is

cos 65 = 35 ÷ x

x = 35 ÷ cos 65

= 83 m


a- 10
b- 70
c- 110
d- 170

Answers

Step-by-step explanation:

step 1. 2x + 50 and 7x are vertical angles

step 2. vertical angles are equal

step 3. 2x + 50 = 7x

step 4. 5x = 50, x= 10

step 5. <AEB = 2x + 50 = 2(10) + 50 = 70.

what is the difference between 1 and o.1978​

Answers

Answer:

0,8022

Step-by-step explanation:

guess it helped

The segments shown below could form a triangle.​

Answers

Answer:

true, they can form a triangle.

Step-by-step explanation:

since, sum of two sides is greater than the third side in any case and the difference between two sides is smaller than the third one in all cases.

Write any
Five Places where ICT
tools can be used.​

Answers

Answer:

A Computer, The Internet, A Printer, Scanners, and Mobile Devices

Step-by-step explanation:

At home, banks, schools, shops and hospitals

6/8X2/6=What is the answer to this equation

Answers

Answer:

6

Step-by-step explanation:

Isabella is cooking a meal for 14 friends. Each person gets
6
of a cup of vegetables.
How many cups of vegetables does Isabella need?

Answers

I’m pretty sure that says 6 cups of vegetables so 84 cups but if you meant 1/6 of a cup then 7/3 cups or 2/1/3

Which expression would be easier to simplify if you used the associative property to change the grouping? O A. (170 + 30) – 41 OB. 3+ (-3) OC. [(-0.1) + (-0.3)] + 2.4 o D. –} + [(-5)+​

Answers

Answer:

A.(170+30)-41

Step-by-step explanation:

(170+30)-41=170+(30-41)

200-41=170+(-11)

159=170-11

159=159

Answer:

D. -2/5 + [(-1/5) + 1/4]

Step-by-step explanation:

Hope it helpss :D

I know how to convert fractions and decimals but the the fact that it’s repeating threw me off so can someone help please?

Answers

The answer is C just took the test for my sister

Answer: It really dosen't matter if its repeating. If it's repeating just put a line ABOVE THE REPEATING PART. I will explain a little bit so you know what I mean.

Step-by-step explanation: So say you divide 2 by 3 your going to get 0.66666666666. You don't have to put all those 6's. All you have to do is put 0.66 with a line above the two sixes. This will indicate you have a repeating decimal. And this works with any repeating number!

I hope this helps!!!!

find the values of x and y

Answers

y=5

x=30

Explanation: since all 3 angles of triangles are marked equal we can see that it is equilateral which means 8y=40 so y=5. Then we can find that the other triangle is an 120 30 30 triangle thus x is 30. You can also do this if you can see straight away that the big triangle is a 30-60-90 triangle and just use 90-60.

A customer at a concession stand bought 2 boxes of popcorn & 3 drinks for $12. Another customer bought 3 boxes of popcorn & 5 drinks for $19. How much does a box of popcorn cost? How much does a drink cost? Write and solve a system of equations Equation 1 : ______________ Equation 2: ______________ Popcorn: _______ Drink: ______

Answers

Answer:

$10 each

Step-by-step explanation:

Does this look right? Explain why


5/6


6.565656…


0.23


-5 3/8

Answers

Answer:

Yes

Step-by-step explanation:

Yes ,a rational number is a number that can be expressed as a fraction. Repeating and terminating decimal are rational number so

5/6 is right since it is a fraction

6.565646 is right since it is a repeating decimal

0.23 is right since it is a terminating decimal

-5 3/8 is right since it is a mixed number

Sqr root of 11 and 0.32416.... is wrong since it creates multiple random unknown digits

simplify the expression, 7 (m + 2 + 5)

Answers

Answer:

7m + 49 or 7(m + 7)

Step-by-step explanation:

Distribute the 7 to each integer and simplify.

Answer:

7m+49

Step-by-step explanation:

7m+14+35

7m+49

Yoshi has a rope 30 feet long. He must cut it in pieces that are 1/4 foot long will he get more or fewer than 30 pieces

Answers

Answer:

More

Step-by-step explanation:

If we divide 30 by .25 we will get 120

A new pair of Nike shoes costs $95. It is on sale for 25% off! How much will you pay (not including taxes)?

Answers

Answer:

23.75

Step-by-step explanation:

95 is the 100 so to find 25% divide it by 4 and you get 23.75

I NEED THE ANSWER TO THIS!!

Answers

Answer:

Step-by-step explanation:

PQ=RS

x-1=3x-7

-2x=-6

x=3

So the length of PS is

x-1+x+3x-7

5x-8, since x=3

5(3)-8

15-8

PS=7

What is the GCF of a¹²b⁴, a⁴b⁸, a²⁴b¹⁶ and a¹²b²⁰?​

Answers

Given:

a¹²b⁴, a⁴b⁸, a²⁴b¹⁶ and a¹²b²⁰.

To find:

The GCF of given terms.

Solution:

Greatest common factor (GCF): To find the GCF of two or more numbers, we need to find the product of their prime factor with their maximum powers.

The given terms are

[tex]a^{12}b^{4},a^{4}b^8, a^{24}b^{16}, a^{12}b^{20}[/tex]

Here, each term has two prime factors a and b. The highest power of a is 24 and the highest power of b is 20. So, the GCF of given terms is

[tex]GCF=a^{24}\times b^{20}[/tex]

[tex]GCF=a^{24}b^{20}[/tex]

Therefore, the GCF of a¹²b⁴, a⁴b⁸, a²⁴b¹⁶ and a¹²b²⁰ is a²⁴b²⁰.

PLEASE..... Need help with questions 5 - 8....

5.
6.
7.
8.

Answers

Answer:

I'm sorry I only know 6 & 7 but... 6 is [tex]y=-\frac{2}{3} x-4[/tex] and 7 is the slope is -5 and the y-intercept is (0,3) and the graph is blurry

Step-by-step explanation:

hope this helps sorry if it doesn't have a good rest of your day :) ❤

Please help with this question

Answers

Answer:

turn 5-4/10 to an improper fraction so

[tex] \frac{54}{10} \times 2[/tex]

you can simply that to

[tex] \frac{54}{5} [/tex]

then change it back to a regular fraction

[tex]10 \frac{4}{5} [/tex] which is also

[tex]10 \frac{8}{10} [/tex]

Answer:

D.  10 [tex]\frac{8}{10}[/tex]

Step-by-step explanation:

54/10 x 2 = 108/10

= 10 [tex]\frac{8}{10}[/tex]

Find an equation of the plane. The plane through the points (0, 9, 9), (9, 0, 9), and (9, 9, 0) Incorrect: Your answer is incorrect.

Answers

Answer:

The equation of the plane is represented by [tex]\frac{1}{18}\cdot x + \frac{1}{18}\cdot y + \frac{1}{18}\cdot z = 1[/tex].

Step-by-step explanation:

Algebraically speaking, a plane can be represented by following vectorial product:

[tex](a,b, c)\,\bullet\,(x,y,z) = 1[/tex] (1)

Where:

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Plane coeffcients.

[tex]x[/tex], [tex]y[/tex], [tex]z[/tex] - Coordinates.

We need three distinct points to determine all coefficients. If we know that [tex](x_{1},y_{1},z_{1}) = (0,9,9)[/tex], [tex](x_{2},y_{2}, z_{2}) = (9,0,9)[/tex] and [tex](x_{3},y_{3},z_{3}) = (9,9,0)[/tex], the system of equations to be solved is:

[tex]9\cdot b + 9\cdot c = 1[/tex] (1)

[tex]9\cdot a + 9\cdot c = 1[/tex] (2)

[tex]9\cdot a + 9\cdot b = 1[/tex] (3)

The solution of this system is [tex]a = \frac{1}{18}[/tex], [tex]b = \frac{1}{18}[/tex], [tex]c = \frac{1}{18}[/tex].

Hence, the equation of the plane is represented by [tex]\frac{1}{18}\cdot x + \frac{1}{18}\cdot y + \frac{1}{18}\cdot z = 1[/tex].

plzzzzz i vill give 5 stars a heart brainlyest if you can anwser this write 5(2j+3+1j)= using the commutive property

Answers

Answer:

The answer would be 5 (3j + 3)

Step-by-step explanation:

The 5 outside the partheness would stay the same

2j + 1j = 3j

The 3 remains the same.

So our answer is

5(3j + 3)

Can someone solve this please

Answers

Answer:15. 5/8 = 0.625

Step-by-step explanation:

n=7, x=4, p=0.45, find p4

Answers

Answer:

1.8

Step-by-step explanation:

All you need to do is use substitution....

p4

They gave us the value of p and it is 0.45, now we need to substitute it, into the expression to find the value

p4 = (0.45)4

0.45 * 4 = 1.8

so p4 = 1.8

Hope this helped!

Have a supercalifragilisticexpialidocious day!

A changes saved
Set up a proportion and use it to solve for x.
2
10
х
3

Answers

Answer:

C. 15

Step-by-step explanation:

The following proportional can be set-up for the figure given:

[tex] \frac{x + 3}{x} = \frac{10 + 2}{10} [/tex]

Solve for x

[tex] \frac{x + 3}{x} = \frac{12}{10} [/tex]

[tex] \frac{x + 3}{x} = \frac{6}{5} [/tex]

Cross multiply

[tex] 5(x + 3) = x(6) [/tex]

[tex] 5x + 15 = 6x [/tex]

15 = 6x - 5x

15 = x

x = 15

1. identify the corresponding sides on the figure below

Answers

Answer:

No because one side is 8 and the other is 18

Step-by-step explanation:

No. The sides are not equal to one another, even in fraction form.

solve and you will get brain list ​

Answers

Answer:

No solutions

Step-by-step explanation:

a wildlife photographer photographs a crocodile and then paddles against a river current for 6 km. Then, hoping to photograph a hippopotamus, she paddles 15 km across a lake. She paddles across the lake for one hour longer than she paddled up the river. find the speed of the boat as she paddles the lake if the river current is 2 km/h. Pls answer. You'll get 100 points.

Answers

Answer:

5 km/h or 6 km/h

Step-by-step explanation:

Let the speed of the boat be xSpeed against the current in the river is x - 2

Time in the river:

6/(x - 2)

Time in the lake:

15/x

The difference:

6/(x - 2) = 15/x - 1

Solve for x to find the speed of the boat

Multiply both sides by x(x - 2) to clear the fraction:

6x = 15(x - 2) - x(x - 2)6x = 15x - 30 - x² + 2xx² - 11x + 30 = 0(x - 5)(x - 6) =0x -5 = 0, x - 6 = 0x = 5 km/h, x = 6 km/h

Answer:

5km/hr or 6km/hr

Step-by-step explanation:

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