# What is Calculus?

Calculus is a branch of mathematics that explores the concepts of change and motion. Developed independently by Isaac Newton and Gottfried Wilhelm Leibniz in the late 17th century, calculus provides a framework for understanding how quantities change and interact. It consists of differential calculus, which focuses on rates of change and slopes, and integral calculus, which deals with accumulation and the concept of area under curves. Widely applied in physics, engineering, economics, and various scientific disciplines, calculus serves as a powerful tool for modeling and solving problems related to dynamic systems and continuous change.

Questions

- What is the inverse function of #f(x) = cosh(x+a/cosh(x+a/cosh(x+cdots)))# with domain and range?
- Consider a linear system whose augmented matrix is first row (1 1 2 | 0) second row (1 2 -3 | -1) third row (9 19 k |-9) For what value of k will the system have no solutions ?
- What is the derivative of #|x|#?
- Differentiate the function. Y= √x(x-8) ?
- Find the absolute maximum and the absolute minimum values of #f(x) = (x + 1)/(x^2 + x + 9)# on the interval #[ 0,∞)#?
- How do I find the antiderivative of #e^(2x) + 1#?
- If #F(x) = sqrt 64 - x^2#, what is f(x)?
- How to find the derivative function of #g(x) = 3/(x-2)#? f(x)= f(x+h)-f(x) / h
- Find the absolute maximum value and the absolute minimum value of #f(x) = x^(4/3) −x−x^(1/3)# on the interval# [−1, 6]#?
- How does calculus relate to computer science?
- How does calculus relate to chemistry?
- How do you prove that the curves of #y=x^x# and y = the Functional Continued Fraction (FCF) generated by #y=x^(x(1+1/y))# touch #y=x#, at their common point ( 1, 1 )?
- The FCF (Functional Continued Fraction) #cosh_(cf) (x;a) = cosh(x+a/cosh(x+a/cosh(x+...)))#. How do you prove that #cosh_(cf) (0;1) = 1.3071725#, nearly and the derivative #(cosh_(cf) (x;1))'=0.56398085#, at x = 0?
- What is the integral of #sqrt(x)#?
- What is the derivative of #sinh(x)#?
- Given #f(x) = cosh(x+a/cosh(x+a/cosh( cdots)))# and #g(x)# its inverse, what is the minimum distance between then for #a > 0#?
- What will be the expansion of #sqrt(x+h)# in powers of #x and h#?
- How do I find the average rate of change of the function from x1 to x2?
- How can calculus be used to optimize manufacturing processes?
- How do I evaluate #int(13 x^2 + 12 x^-2)dx#?