Can derivatives be defined without a limit (as are integrals defined in Apostol's Calculus)
125615
Defining the derivative without limits
143874
Limit of derivative is zero. Does it imply a limit for f(x)?
112402
Series - Apostol Calculus Vol I, Section 10.20 #24
105767
derivative under integral intuition
98306
Limit of $n/\ln(n)$ without L'Hôpital's rule
44336
Is $\lim\limits_{x\to x_0}f'(x)=f'(x_0)$?
151314
What does it mean to differentiate in calculus?
5295
Can the graph of a bounded function ever have an unbounded derivative?
68752
A few questions about infinite derivative.
117338
Counterexample to second derivative test when f''(x) is not continuously differentiable
119907
Finding the Derivative of |x| using the Limit Definition
89421
Does $\int_{1}^{\infty} g(x)\ dx$ imply $\lim\limits_{x\to \infty}g(x)=0$?
96589
Word Question Involving the Definition of the Derivative
140884
Limits and derivatives - two questions
117613
Interchange of partial derivative and limit
76249
Does the limit of function of two variables exist
78444
Limit of definite integral of $f(x)\cos(mx)$