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
Ket [755]
3 years ago
9

Find the linear approximation of the function g(x) = 3 root 1 + x at a = 0. g(x). Use it to approximate the numbers 3 root 0.95

and 3 root 1.1.
Mathematics
1 answer:
Virty [35]3 years ago
7 0

Answer:

L(x)=1+\dfrac{1}{3}x

\sqrt[3]{0.95} \approx 0.9833

\sqrt[3]{1.1} \approx 1.0333

Step-by-step explanation:

Given the function: g(x)=\sqrt[3]{1+x}

We are to determine the linear approximation of the function g(x) at a = 0.

Linear Approximating Polynomial,L(x)=f(a)+f'(a)(x-a)

a=0

g(0)=\sqrt[3]{1+0}=1

g'(x)=\frac{1}{3}(1+x)^{-2/3} \\g'(0)=\frac{1}{3}(1+0)^{-2/3}=\frac{1}{3}

Therefore:

L(x)=1+\frac{1}{3}(x-0)\\\\$The linear approximating polynomial of g(x) is:$\\\\L(x)=1+\dfrac{1}{3}x

(b)\sqrt[3]{0.95}= \sqrt[3]{1-0.05}

When x = - 0.05

L(-0.05)=1+\dfrac{1}{3}(-0.05)=0.9833

\sqrt[3]{0.95} \approx 0.9833

(c)

(b)\sqrt[3]{1.1}= \sqrt[3]{1+0.1}

When x = 0.1

L(1.1)=1+\dfrac{1}{3}(0.1)=1.0333

\sqrt[3]{1.1} \approx 1.0333

You might be interested in
PLEASE HELP WORTH 50 POINTS
VashaNatasha [74]

Answer:cos( A + B ) = cosAcosB - sinAsinB ;

cos( A + B ) / ( cosAsinB ) = ( cosAcosB - sinAsinB ) / ( cosAsinB ) = ( cosAcosB ) / ( cosAsinB ) - ( sinAsinB ) / ( cosAsinB ) = cosB / sinB - sinA / cosA = cotB - tanA ;

                     

tan²(x) - sin²(x) = sin²(x)/cos²(x) - sin²(x)

… = sin²(x) (1/cos²(x) - 1)

… = sin²(x) (sec²(x) - 1)

… = sin²(x) tan²(x)

Step-by-step explanation:

5 0
2 years ago
C(-6, 5) and D(-3, 1). find the distance between the two points
Marat540 [252]
The distance is d=5.0
5 0
3 years ago
Quadrilateral ABCD is translated down and left to form quadrilateral OLMN. If AB = 6 units, BC = 5 units, CD = 8 units, and AD =
olga2289 [7]
6 units. AB and LO are congruent sides, and if AB= 6 units, then LO would be the same.
6 0
3 years ago
Read 2 more answers
Store A charges $1,200 for repairs with a 6 percent sales tax. Store B charges $1,350 with a 7 percent sales tax. Explain how yo
Lilit [14]

Answer:

The total repair cost for each store is the cost of repairs added to the sales tax. The amount of money saved will be the difference between the two total costs.

6 0
3 years ago
Read 2 more answers
A function is a type of ____.<br> a. vertical line test <br> b. relation<br> c. range <br> d. domain
Nimfa-mama [501]
It’s a type of range
4 0
3 years ago
Other questions:
  • what is 7543762587646537659870970576434326 + 478964654513214375887o876u5464654353547566 divided by 9834790 x 4676696746436587697
    13·2 answers
  • Rewrite the radicand as two factors, one of which is a perfect cube.
    14·2 answers
  • Which equations will help you solve this problem? There are 18 muffins on a plate. If they are split equally among 9 people, how
    15·1 answer
  • Which equation has no solution?
    12·1 answer
  • Which of the following segments is a radius of circle O?
    14·2 answers
  • How many kilometers are equivalent to 3,570 meters?
    11·1 answer
  • Marie purchased a $49.00 gift for a baby shower. She uses a coupon that offers 20% off. How much will Marie spend on the gift af
    12·2 answers
  • Solve the inequality for v.<br>3v-37&gt;-2(8-5v)<br>Simplify your answer as much as possible.​
    8·1 answer
  • Which angle in the diagram is obtuse
    15·1 answer
  • PLEASE HELP!!!!! BRAINLIEST!! I will give brainliest if you answer, I will also give brainliest ON ALL QUESTIONS!! if you go to
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!