Which of the following statements is true about continuous functions?
Practice Questions
1 question
Q1
Which of the following statements is true about continuous functions?
They can be differentiated everywhere
They are always bounded
They can be integrated
They can have jump discontinuities
Continuous functions can be integrated over an interval, but they are not necessarily differentiable or bounded.
Questions & Step-by-step Solutions
1 item
Q
Q: Which of the following statements is true about continuous functions?
Solution: Continuous functions can be integrated over an interval, but they are not necessarily differentiable or bounded.
Steps: 4
Step 1: Understand what a continuous function is. A continuous function is one where you can draw the graph without lifting your pencil from the paper.
Step 2: Know that continuous functions can be integrated. This means you can find the area under the curve of the function over a certain interval.
Step 3: Learn that continuous functions are not always differentiable. Differentiable means you can find the slope of the function at every point. Some continuous functions have sharp corners or cusps where they are not differentiable.
Step 4: Recognize that continuous functions are not necessarily bounded. A bounded function stays within a certain range, while an unbounded function can go to infinity.
