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
Elanso [62]
2 years ago
13

From first principles, find the indicated derivatives​

Mathematics
1 answer:
LenaWriter [7]2 years ago
6 0

By definition of the derivative,

\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac{\left(\frac{(s + h)^3}2 + 1\right) - \left(\frac{s^3}2 + 1\right)}{h}

\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac{\left(\frac{s^3+3s^2h+3sh^2+h^3}2 + 1\right) - \left(\frac{s^3}2 + 1\right)}{h}

\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac{\frac{3s^2h+3sh^2+h^3}2}{h}

\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac12 \frac{3s^2h+3sh^2+h^3}{h}

\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac12 (3s^2+3sh+h^2)

\displaystyle\frac{dr}{ds} = \frac{3s^2}2

You might be interested in
Plz can someone help me with number 5?
Anettt [7]

Answer:

77

Step-by-step explanation:Trust

7 0
3 years ago
Which is a factor of 21 <br> a6 <br> b5 <br> c4 <br> d3
aev [14]
3 because 7*3=21,...........
6 0
3 years ago
Read 2 more answers
What are the parts of an algebraic expression, and how do they relate to polynomial expressions?
Arlecino [84]

The parts of algebraic expressions related to polynomials are variables and coefficients.

<h3>What are the parts of algebraic expressions?</h3>

The parts of algebraic expressions are;

  • Variables which are letters that represent numbers
  • Coefficients are numbers that multiply the variables
  • Constant is a number that is not multiplied by any variable

Polynomials are algebraic expressions composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, and multiplication

Polynomials consists of variables and coefficients. The variables in polynomials are also called indeterminates. The coefficients also multiply this variables.

Thus, the parts of algebraic expressions related to polynomials are variables and coefficients.

Learn more about algebraic expressions here:

brainly.com/question/4344214

#SPJ1

3 0
2 years ago
Given isosceles trapezoid TRHY, in units what is the length of b2 if the height is 13 units, b1 is 21 units, and the area is 215
GenaCL600 [577]

We are given a trapezoid TRHY.

Height of the trapezoid = 13 units.

b1 = 21 units and

Area = 215 units squares.

We need to find the length of b2.

We know formula for area of a trapezoid.

A= \frac{1}{2} (b1+b2)\times h

Plugging values in formula.

215 = \frac{1}{2}(21+b2)× 13.

215 = 6.5(21+b2)

Dividing both sides by 6.5, we get

\frac{215}{6.5}=\frac{6.5(21+b2)}{6.5}

33.08 = 21+b2.

Subtracting 21 from both sides, we get

33.08-21 = 21-21+b2

b2 = 12.08.

<h3>Therefore,  length of b2 is 12.08 units.</h3>
4 0
3 years ago
Brainly.com fam help me fine the value of the x thank you so much
Thepotemich [5.8K]
First you subtract 47 from both sides (-47 from 47 and -47 from 32)
Then you get -3x = -15
Divide -3 from -3x and -3 from -15
Leaving you with X = 5
5 0
3 years ago
Other questions:
  • Mariana, Pamela y Nancy decidieron comprar una consola de video juegos X Box y acordaron que cada una aportará 1/3 parte del cos
    15·1 answer
  • Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions.
    14·2 answers
  • Make p the subject, 4(p - 2q) = 3p + 2
    6·1 answer
  • I really need help with these three questions, urgent!
    11·1 answer
  • PLEASE HELP!!!! ASAPP!!!! I will name Brainliest.
    6·1 answer
  • Enya is building a storage cupboard in the shape of a rectangular prism. The rectangular prism has a square base with side lengt
    10·1 answer
  • Help please Brainiest to whoever is correct
    8·2 answers
  • A person earns 12% of their monthly salary at their part time job. If their full time job pays $3,696 monthly, how much money do
    12·2 answers
  • What is the average rate of change for this quadratic function for the interval fr x=2 to x=4?
    9·1 answer
  • This exercise uses, the population growth model
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!