1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zloy xaker [14]
3 years ago
13

T what point does the curve have maximum curvature? Y = 7ex (x, y) = what happens to the curvature as x → ∞? Κ(x) approaches as

x → ∞.
Mathematics
1 answer:
Nookie1986 [14]3 years ago
5 0

Formula for curvature for a well behaved curve y=f(x) is


K(x)= \frac{|{y}''|}{[1+{y}'^2]^\frac{3}{2}}


The given curve is y=7e^{x}


{y}''=7e^{x}\\ {y}'=7e^{x}


k(x)=\frac{7e^{x}}{[{1+(7e^{x})^2}]^\frac{3}{2}}


{k(x)}'=\frac{7(e^x)(1+49e^{2x})(49e^{2x}-\frac{1}{2})}{[1+49e^{2x}]^{3}}

For Maxima or Minima

{k(x)}'=0

7(e^x)(1+49e^{2x})(98e^{2x}-1)=0

→e^{x}=0∨ 1+49e^{2x}=0∨98e^{2x}-1=0

e^{x}=0  ,  ∧ 1+49e^{2x}=0   [not possible ∵there exists no value of x satisfying these equation]

→98e^{2x}-1=0

Solving this we get

x= -\frac{1}{2}\ln{98}

As you will evaluate {k(x})}''<0 at x=-\frac{1}{2}\ln98

So this is the point of Maxima. we get y=7×1/√98=1/√2

(x,y)=[-\frac{1}{2}\ln98,1/√2]

k(x)=\lim_{x\to\infty } \frac{7e^{x}}{[{1+(7e^{x})^2}]^\frac{3}{2}}

k(x)=\frac{7}{\infty}

k(x)=0







You might be interested in
Complete the equation of the line through <br><br>(-8, 8,) and (1, -10)
Dahasolnce [82]

Answer:

Equation of a line has form of y = ax + b

This line passes (-8, 8) and (1, 10), then:

-8 = -8 x a + b

10 = a + b

Subtract 2nd equation to 1st equation, then:

18 = 9 x a

=> a = 2

=> b = 10 - 2 = 8

=> y = 2x + 8

Hope this helps!

:)

6 0
2 years ago
Which ratio expresses the scale used to create this drawing?
nevsk [136]
The answer is D















Really hoped this helped <3
5 0
2 years ago
Which expression is equivalent to (2x + 3)2 – 5?
ddd [48]
4x+6-5
turns into 4x+1
5 0
2 years ago
Which angle is an exterior angle of the triangle?
svetoff [14.1K]

Answer:

Angle 4

Step-by-step explanation:

Exterior is the angle that is on the outside of the triangle.

8 0
3 years ago
Read 2 more answers
Please help asap 20 pts
kherson [118]

It is associative property

8 0
3 years ago
Other questions:
  • Graph f(x)=34x+2f(x)=34x+2.
    7·1 answer
  • Lim x→25 x−25 /√x−5
    8·1 answer
  • 2 Points
    8·1 answer
  • What is the best estimate for 48% of 199
    9·2 answers
  • 2(8-y)<br> Distributive property
    15·2 answers
  • Find the mode of the following distribution
    14·1 answer
  • I NEED HELP PLEASE, THANKS! :) Write the augmented matrix for the system of linear equations. –9w + x + 8y + 2z = –6 –5x + 9y –
    5·1 answer
  • Can someone please answer this quick i have no idea how this app works but I need a quick answer
    11·2 answers
  • Last month the cost of using the air pump at a garage was 20p.
    9·1 answer
  • Find the x-intercept and y-intercept of the equation: 3x-y = -9
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!