SammyS said:1. b is false.
Is f(x) positive ?
I'll look at the other problem soon.
SammyS said:The second link looked OK to me.
deluks917 said:Its possible your professor wants you to write out your steps a bit more.
Limits in analysis refer to the value that a function approaches as its input variable approaches a particular value. It is used to describe the behavior of a function near a specific point and is an essential tool in calculus and mathematical analysis.
A function is strictly increasing if for any two points on the graph, the y-value of the second point is greater than the y-value of the first point. This means that as the input variable increases, the output variable also increases without any dips or plateaus. To determine if a function is strictly increasing, you can take the derivative of the function and check if it is always positive.
Differentiability is a key concept in analysis that describes the smoothness of a function. A function is differentiable at a point if it has a well-defined derivative at that point. This allows us to study the behavior of a function and its rates of change, which is essential in many real-world applications.
The derivative of a function is a measure of its instantaneous rate of change. It can be found by taking the limit of the difference quotient as the distance between two points on the graph approaches zero. Alternatively, you can also use differentiation rules and techniques to find the derivative of a function.
Yes, a function can be continuous at a point but not differentiable at that point. This occurs when the function is not smooth or has a sharp corner or cusp at that point. A classic example is the absolute value function, which is continuous but not differentiable at x=0.