Practice Introduction To Numerical Differentiation And Integration (3.1) - Numerical Differentiation and Integration

Practice: Introduction to Numerical Differentiation and Integration

Lesson 3.1Numerical Differentiation and Integration

Practise this section

9 questions

Flashcard drill
2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What is numerical differentiation?
Show hintHide hint
Think about how derivatives are generally defined.
Question 2.
List the three finite difference methods.
Show hintHide hint
Consider how each method approaches the problem.
3Question 3.
What is the primary goal of numerical differentiation?
- To find exact derivatives
- To approximate derivatives
- To calculate integrals
Show hintHide hint
Consider the cases when you might not have a formula.
4Question 4.
True or False: The central difference method is less accurate than the forward difference method.
- True
- False
Show hintHide hint
Think about the data points used in each method.
Question 5.
Given the function f(x) = x^2 + 3x, find the derivative using forward and backward differences at x = 1 with h = 0.1. Compare your results to the actual derivative.
Show hintHide hint
Use the provided formulae and plug in the values carefully.
Question 6.
Estimate the integral of f(x) = cos(x) from 0 to π/2 using Simpson's Rule with four intervals. Calculate the error compared to the known analytical result.
Show hintHide hint
Divide the interval properly and remember to apply the Simpson's Rule formula.

5 more questions in this section. Enroll free to practise them all.