Calculus 1 problems: functions, integrals, series

In summary, the conversation is about someone doing older exams and seeking help to confirm their solutions. The mentor suggests trying to check the solutions themselves and provides tips for the questions, which are slightly more involved than True/False questions.
  • #1
BigBowler
2
0
Mentor note: Moved from technical section, so is missing the homework template.
Im doing some older exams that my professor has provided, but I haven't got the solutions for these. Can someone help confirm that the solutions I've arrived at are correct?

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  • #2
For these problems, it's probably better if you take a stab at checking them for yourself. For the first question, could the answer be B or C? For the second question, test each given function to see if it's a solution of the diff. equation. For the third and fourth questions, I would use the Ratio Test to determine the interval on which each series converges.
 
  • #3
Thanks for the tips.
 
  • #4
The questions are slightly more involved than True/False questions, as they really have only three reasonable answers. If you give a D response (Don't know), that's saying to the instructor that you really don't have a clue.
 

What is the purpose of studying Calculus 1?

The purpose of studying Calculus 1 is to understand the fundamental concepts and techniques of calculus, which is the branch of mathematics that deals with rates of change and accumulation. It is an essential tool for solving real-world problems in fields such as physics, engineering, economics, and more.

What are functions in Calculus 1?

Functions in Calculus 1 refer to mathematical relations that map input values to output values. They are represented by equations and can be used to model various phenomena such as motion, growth, and decay. In calculus, functions are studied in terms of their rates of change and the behavior of their graphs.

What are integrals in Calculus 1?

Integrals in Calculus 1 are mathematical tools used to find the area under a curve. They are also used to calculate the volume of irregular shapes and to solve problems involving accumulation, such as finding the total distance traveled or the total amount of a substance in a given time period. Integrals are the inverse operation of derivatives.

What are series in Calculus 1?

Series in Calculus 1 refer to an infinite sum of terms. They are used to represent functions that cannot be expressed by a finite number of terms, and to approximate functions that are difficult to integrate. Series are also used to study the convergence and divergence of sequences and to solve various types of mathematical problems.

How can I improve my understanding of Calculus 1?

To improve your understanding of Calculus 1, it is important to practice solving problems and to seek help from your instructor or classmates when needed. It is also helpful to review the fundamental concepts and to make connections between different topics in calculus. Additionally, using online resources and seeking out additional practice problems can also aid in improving your understanding of Calculus 1.

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