Solutions to 4 Math Problems: Derivatives & Integrals

  • Thread starter Jacobpm64
  • Start date
In summary, the conversation is a follow-up post for problems posted yesterday. The problems include finding the derivative and integrals, with the poster believing they have the correct answers. The expert points out an error in the algebra for the derivative problem and confirms that the integrals are correct. The poster makes a correction and the expert confirms that the new derivative is correct. The conversation ends with a thank you from the poster.
  • #1
Jacobpm64
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This is a followup post for all the problems i posted yesterday.. please check them all.. i believe i got the correct answers.. Thanks a lot.

1. Find the derivative:
http://img225.imageshack.us/img225/7261/der42complete4fy.gif

2. Find the integral:
http://img195.imageshack.us/img195/1766/int18complete2ua.gif

3. Find the integral:
http://img225.imageshack.us/img225/7525/int20complete0pr.gif

4. Find the integral:
http://img225.imageshack.us/img225/3107/int26complete9ld.gif
 
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  • #2
Jacobpm64 said:
This is a followup post for all the problems i posted yesterday.. please check them all.. i believe i got the correct answers.. Thanks a lot.

1. Find the derivative:
http://img225.imageshack.us/img225/7261/der42complete4fy.gif
Before taking the derivative, the algebra is wrong. You must *divide* by x-2 whereas you multiplied by x-2. (I know that you were probably thinking of (-x-2) divided by (x*(x-1)/(x-2)) but what you have is instead (-x-2)/(x*(x-1)) divided by (x-2)
 
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  • #3
Jacobpm64 said:
This is a followup post for all the problems i posted yesterday.. please check them all.. i believe i got the correct answers.. Thanks a lot.


The integrals are right (except that one would never write u^0/0 in the last one!)
 
  • #4
ah, i forgot the reciprocal.. grr.. give me a few minutes.. i'll correct that and repost..
 
  • #5
here is a fix on the derivative one.. is this right now?

http://img100.imageshack.us/img100/4594/der42complete1ag.gif
 
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  • #6
Looks good.
 
  • #7
Jacobpm64 said:
here is a fix on the derivative one.. is this right now?

http://img100.imageshack.us/img100/4594/der42complete1ag.gif
[/URL]

Looks right to me
 
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  • #8
thanks :biggrin:
 

FAQ: Solutions to 4 Math Problems: Derivatives & Integrals

What are derivatives and integrals?

Derivatives and integrals are mathematical operations used to determine the rate of change of a function and the area under a curve, respectively. Derivatives measure the instantaneous rate of change at a specific point, while integrals calculate the cumulative effect of change over a given interval.

Why are derivatives and integrals important in mathematics?

Derivatives and integrals are fundamental concepts in calculus and are widely used in many fields of science and engineering. They provide tools for solving problems involving rates of change and accumulation, making them essential in understanding complex systems and phenomena.

How do you find derivatives and integrals?

Derivatives can be found using the rules of differentiation, such as the power rule, chain rule, and product rule. Integrals can be evaluated using techniques such as substitution, integration by parts, and partial fractions. In some cases, computer software or calculators can also be used to find derivatives and integrals.

What are some real-world applications of derivatives and integrals?

Derivatives are used in physics to calculate velocity and acceleration, in economics to determine marginal cost and revenue, and in biology to model population growth. Integrals are used in engineering to calculate work and power, in finance to determine compound interest, and in statistics to find areas under probability curves.

Are there any common mistakes to avoid when using derivatives and integrals?

Some common mistakes when using derivatives include not checking for special cases, such as points of discontinuity or undefined points, and not simplifying the final answer. For integrals, common mistakes include forgetting to include the constant of integration and not checking the bounds of integration. It is important to double-check calculations and pay attention to detail when working with derivatives and integrals.

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