: Find the equation of the tangent line to the curve f(x)= e^xat x_0= 2, and show this line on the graph.

Answers

Answer 1

The tangent line to f(x) = e ˣ at the point x = 2 has slope equal to f ' (2):

f(x) = e ˣ   →   f '(x) = e ˣ   →   f ' (2) = e ²

At x = 2, the function takes on a value of f (2) = e ². Use the point-slope formula to get the equation of the tangent line:

y - e ² = e ² (x - 2)

Solve for y :

y = e ² x - e ²


Related Questions

Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places. y = e−x^2, y = 0, x = −2, x = 2​

Answers

Y = 4x*e^(-x) , y=0, x=3 , rotation about y-axis
Graph or sketch the function.
The volumeelement is a cylinder with radius x height y and thickness dx.
Integrate from x=0 to x=3
V = 2 π ∫x*y dx =
2 π ∫x*4x*e^(-x) dx
8 π ∫x²*e^(-x) dx ,
Integrate by part: ∫e^(-x)*x² dx , let u’ = e^(-x) => u = -e^(-x) and v = x² => v’ = 2x
∫e^(-x)*x² dx = -e^(-x)*x² + ∫e^(-x)*2x dx
Integrate by part: ∫e^(-x)*2x dx = -e^(-x)*2x + ∫e^(-x)*2 dx
∫2e^(-x) dx = -2e^(-x).
If we wrap up the above we get :
V = 8 π*[-e^(-x)*(x²+2x+2)]
V = 8 π*[e⁻³(9+6+2) – (-e⁰ *2)]
V = 8 π*[17*e⁻³+ 2] = 28.99363 v.u.

Please help me find the surface area!

Answers

Answer: question 9 COULD be 240 and 12. might be 2880

Step-by-step explanation:

What is the y-value of the vertex of the function f(x)=−(x+8)(x−14)? 3 6 112 121

Answers

Answer:

121

Step-by-step explanation:121 ! just got it right.

Answer:

D)

Step-by-step explanation:

on edge

A dealer buys articles for R7500 and makes the price 30% higher.
What is the selling price of the articles?​

Answers

Answer:

9750

Step-by-step explanation:

profit amount = 30% of R 7500

= 30/100 *R 7500

= 2250

now

sp = R 7500 + R 2250

= R 9750

A lab orders a number of chemicals from the same supplier every 10 days. The lead time is six days. The manager of the lab must determine how much of one of these chemicals to order. Check of stock reviewed that 9 25-milliliter (ml) jars are on hand. Daily usage of the chemical is appropriately normal with a mean of 16 ml per day and a standard deviation of 3.5 ml per day. The desired service level for this chemical is 95%. a) How many jars of the chemical should he ordered

Answers

Answer:

3 jars of the chemical should be ordered

Step-by-step explanation:

Given the data in the question;

Ol = 10 days

d = 16 ml

z = 1.65 at 95% service level

σ = 3.5 ml

Check of stock reviewed that 9 of 25-milliliter (ml) jars are on hand

so inventory in position = 9 × 25 = 225 ml        

now,

since this is a fixed-order-internal system;

first we determine our Target inventory

Target inventory = 16 × ( 10 + 6) + 1.65√( 10 + 6 ) × 3.5

Target inventory = 265 + 23.1  

Target inventory = 288.1

so  

Amount to order = Target inventory - inventory in position

Amount to order = 288.1 - 225  = 63.1 ml

∴ number of jars to order will be;

⇒ 63.1  ml/ 25 ml = 2.5  { approximately 3 jars }

Therefore, 3 jars of the chemical should be ordered

Help. I have no idea what to do

Answers

Answer: The answer is to ask your parents because something is definitely wrong with your teacher to give such a hard sun to solve like that.

Step-by-step explanation:  sorry man that hard.

Solve.
b + 2/9 = 1 3/5

Answers

Exact form
B=107/45
Decimal form
B=2.36
Mixed number form
B=2:17/45

Help please (50 point) sorry hhh

Answers

Answer:

7.5

Step-by-step explanation:

The actual fraction is 15/2, which is equivlent to 7.5

Im pretty sure its infinite solutions

shin godzilla vs zilla​

Answers

Answer:

I'd say zilla

Step-by-step explanation:

shin Godzilla would win because here is one scenario Zilla jumps on his back biting him then Shin Godzilla shoots his back beams killing him. plus Zilla shots only fire not any of the radiation things

Paige only needs to sell to 17 more customers to receive a bonus. She works part time, so she only talks to 50 customers per day. With a sales ratio of 1:9, on which day will Paige qualify for a bonus?

Answers

Answer:

Paige will qualify for a bonus on her 4th day of work.

Step-by-step explanation:

50 customers per day

needs to sell to 17

Ratio = 1:9

      1:9

×17         ×17

    17:153

Paige needs to see 153 customers.

153 ÷ 50 = 3.06 ≈ 4   (As the answer is not asking for the exact number of the day you round up to make a whole day without underestimating)

So, Paige will qualify for a bonus on her 4th day of work.

BEEN ASKING FIR AN HOUR: A rectangle's length is 3 feet shorter than 4 times the width. If we use w to represent the rectangle's width, use a polynomial to represent the rectangle's area in expanded form.​

Answers

Answer:

Step-by-step explanation:

w is the width of the rectangle, then the length would be 4w - 3.

A = lw

A = w(4w -3)

A =4w² - 3w

Hope this helped!!!

Question 4
Which expression represents f-(x) if f(x) = 11 – 10x ?

Answers

Answer:

hhuhhuhhhuhh

Step-by-step explanation:

I will give BRAINLIST Solve the quadratic function by factoring.

2x^2+7x-4=0


Someone please help I will give BRAINLIST please show work I need this for my test

Answers

(2x+1)(x-4)=0
x-4=0
2x+1=0
X= -1/2 , 4

Need help please and thank you

Answers

Answer:

B is your answer

Step-by-step explanation:

there is none but GOOD LUCK

Problem of the week, provide step-by-step please!

Answers

Answer:

Step-by-step explanation:

The smallest perfect square that has three different prime numbers as factor is 900

900 = 30 * 30

Factors = 2² * 3² * 5² = 900

a clothing manufacturer makes coats, shirts and slacks. The time required for The Cutting, sewing, and packaging on each item is shown in the table. How many of each should be made to use all available labor hours?​

Answers

9514 1404 393

Answer:

  120 coats, 200 shirts, 180 slacks

Step-by-step explanation:

If we let c, s, p represent quantities of coats, shirts, pants, respectively, then the total number of minutes required for cutting, sewing, and packaging can be expressed by ...

  20c +15s +10p = 7200

  60c +30s +24p = 17520

  5c +12s +6p = 4080

These equations can be written in "augmented matrix" form and submitted to your friendly local matrix solver (online or on your calculator). You would ask for "reduced row-echelon form". The calculator function that accomplishes this is often called RREF. The matrix and result are ...

  [tex]\left[\begin{array}{ccc|c}20&15&10&7200\\60&30&24&17520\\5&12&6&4080\end{array}\right]\rightarrow \left[\begin{array}{ccc|c}1&0&0&120\\0&1&0&200\\0&0&1&180\end{array}\right][/tex]

This means production should be of ...

  120 coats, 200 shirts, 180 slacks

Select the measures that are equal. Select all that apply.pls help me i beg you

Answers

D, B, and F are equal

The life of light bulbs is distributed normally. The standard deviation of the lifetime is 15 hours and the mean lifetime of a bulb is 590 hours. Find the probability of a bulb lasting for at most 605 hours. Round your answer to four decimal places.

Answers

Answer:

0.8413 = 84.13% probability of a bulb lasting for at most 605 hours.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

The standard deviation of the lifetime is 15 hours and the mean lifetime of a bulb is 590 hours.

This means that [tex]\sigma = 15, \mu = 590[/tex]

Find the probability of a bulb lasting for at most 605 hours.

This is the pvalue of Z when X = 605. So

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

[tex]Z = \frac{605 - 590}{15}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413

0.8413 = 84.13% probability of a bulb lasting for at most 605 hours.

Experts believe that 70% of adults in the United States believe it is more enjoyable to be married than single. An ABC News Poll in 2004 surveyed 1,501 randomly selected adults in the United States and asked if they believed it is more enjoyable to be married or single. In the survey, 1,126 people responded that it is more enjoyable to be married.
Choose the best description.
a. All U.S. adults
b. The 1,501 U.S. adults referred to in this problem
c. The 1,126 U.S. adults referred to in this problem
d. All U.S. adults who believe it is more enjoyable to be married than single

Answers

Answer:

D. all U.S adults who believe it is more enjoyable to be married than single

Step-by-step explanation:

Sana nakatulong

Please help me out with this question

Answers

Answer:

43200

Step-by-step explanation:

2(60*80)

2(80*120)

2(60*120)

add that up

Answer:

43,200

Step-by-step explanation:

I used a surface area calculator, but the formula it gives is

A (2wl+hl+hw), w is width, h is height and l is length. Hope this helps!

The blue segment below is a radius of oo. What is the length of the diameter of the circle?

Answers

Answer:

Diameter = 25.4 units

Step-by-step explanation:

radius = 12.7

Diameter = 2 × radius

= 2 × 12.7

= 25.4 units

D

Step:
Length of diameter = 2* radius = 2*12.7= 25.4


How much money would you have to invest at 9% compounded semiannually so that the total investment has a value of $2,090 after one year?

Answers

Answer:

Im just doing this for points .,.

Step-by-step explanation:

can anyone answer these? it would be appreciated:)

Answers

Answer:

Step-by-step explanation:

student were asked to choose their favorite subject if 4/8 of the student chose history and 3/8 chose biology what fraction chose either history or biology

Answers

Answer:

7/8

Step-by-step explanation:

Answer:

4/5

Step-by-step explanation:

What is the value of 6 in the number 762

Answers

Answer:

60

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

Hi,

Since the 6 is in the tenths place, it's a 60.

I hope this helps :)

graphing sucks
ugh. but anyway does anybody know how to graph using only an equation? please explain thoroughly. PLEASE SAVE MY LIFE!​

Answers

- you can substitue x and y for 1, or 0 and graph each point

- use desmos and copy it

- depending on the type of equation find the x-intercept, y-intercept, vertex and then draw a line between them

_____ ÷ r × r = p
be fast :) easy point for who ever get it

Answers

Answer:

p

Step-by-step explanation:

lol question unclear

Answer:

p

Step-by-step explanation:

if you divide a number by a number and then multiply that same number by that number it is 1. so it is just __=p

Hope that helps :)

During trimester 2 the math team gave 4 product assignments. The 4 scores were a 50, 90, 62, and 63.
What was the median score of the product assignments?
What was the average score of the product assignments?

Answers

Answer:

median = 62.5, average = 66.25

Step-by-step explanation:

50, 90 , 62 and 63

median = 50 , 62, 63, 90

62 + 63 / 2

125/2

median = 62.5

average = 50 + 90 + 62 + 63 /4

=265/4

average = 66.25

solve the equation on the interval [0,2}. 5 cos x - root 3 = 3 cos x

Answers

Answer:

Step-by-step explanation:

5 cos x-√3=3 cos x

5 cos x-3 cos x=√3

2 cos x=√3

cos x=√3/2=cos π/6,cos (2π-π/6)

x=π/6,11π/6

Answer:x=π/6,11π/6

Step-by-step explanation:

5 cos x-√3=3 cos x

5 cos x-3 cos x=√3

2 cos x=√3

cos x=√3/2=cos π/6,cos (2π-π/6)

x=π/6,11π/6

K
Given that m_JKL = 94º, m_KL) = 41°, and the radius of the circle is 10 units, find s, rounded to the nearest hundredth.
units
S=
Reset
Next
tum. All rights reserved.
1

Answers

Step-by-step explanation:

angle j + angle JKL + angle KLJ = 180(sum of angles in a triangle)

[tex]j + 94 + 41 = 180 \\ j + 135 = 180 \\ j = 180 - 135 \\ = 45[/tex]

Arc Length s =

given r = 10 units,

[tex] = (\frac{j}{360} ) \times 2\pi \: r \\ = ( \frac{45}{360} ) \times 2\pi(10) \\ = 0.125 \times 20\pi \\ = 2.5\pi \\ = 7.85units(nearest \: hundredth)[/tex]

Answer:

7.85 units

Hope this helped and have a good day :D

Other Questions
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Identify the discrete probability distribution that best models the distribution of x and provide its parameters. (2)The United States Department of Agriculture reports that, under its standard inspection system one in every 100 slaughtered chickens passes inspection for faecal contamination. Find the probability that, in a random sample of 6 slaughtered chickens, at least one passes inspection for faecal inspection. (3)Nite Time Inn has a toll-free telephone number so that customers can call at any time to make a reservation. A typical call takes about 4 minutes to complete, and the time required follows an exponential distribution. Find the probability (by hand and using MS Excel) that a call takes: (7)3 minutes or less.exceed 5 minutes.Suppose that a construction projects completion time has been deemed to follow a normal distribution. Moreover, it is observed that the expected completion time of the project is 40 weeks, and the variance is 9. 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