CALCULUS I - hi
https://notendur.hi.is/adl2/CalcI_Complete.pdfDifferentiation Formulas – Here we will start introducing some of the differentiation formulas used in a calculus course. Product and Quotient Rule – In this section we will took at differentiating products and quotients of functions. Derivatives of Trig Functions – We’ll give the derivatives of the trig functions in this section.
Chapter 5: Limits, Continuity, and Differentiability
www.kquattrin.com › 2/5/8 › 75.1: Limits, L’Hopital’s Rule, and The Limit Definitions of a Derivative As mentioned in the intro to this chapter and last year, the limit was created/defined as an operation that would deal with y-values that were of an indeterminate form. x→a lim f(x) is read "the limit, as x approaches a, of f of x." What the definition
Continuity and Differentiability 31.12.08
www.ncert.nic.in › textbook › pdf(to be read as: the right hand limit of f(x) at 0 is plus infinity). We wish to emphasise that + ∞ is NOT a real number and hence the right hand limit of f at 0 does not exist (as a real number). Similarly, the left hand limit of f at 0 may be found. The following table is self explanatory. Table 5.2
LIMITS AND DERIVATIVES
ncert.nic.in › ncerts › lf (x) with x > 0 equals 2, i.e., the right hand limit of f (x) at 0 is 0 lim ( ) 2 x fx → + = . In this case the right and left hand limits are different, and hence we say that the limit of f (x) as x tends to zero does not exist (even though the function is defined at 0). Summary We say lim x→a– f(x) is the expected value of f at x = a ...
Continuity and Differentiability 31.12.08
https://www.ncert.nic.in/textbook/pdf/lemh105.pdf150 MATHEMATICS Solution The function is defined at x = 0 and its value at x = 0 is 1. When x ≠ 0, the function is given by a polynomial. Hence, 0 lim ( ) x f x → = 3 3 0 lim ( 3) 0 3 3 x x → + = + = Since the limit of f at x = 0 does not coincide wit h f(0), the function is not continuous at x = 0. It may be noted that x = 0 is the only point of discontinuity for this function.