sql server reporting services barcode font tan x x x3 in Software

Generate QR Code in Software tan x x x3

x 0

Limit[(1 + Sin[x])Cot[2x], x 0]

1/x Limit[(Exp[x]+ x) , x ]

1/x Limit[(Exp[x]+ x) , x ] 1

8.5 Compute lim(2 x )

x 1

tan( x ) 2

Limit[(2 x)Tan[ 2 x], x 1] 2/

8.6 If p dollars is compounded n times per year at an annual interest rate of r, the money will be worth nt r p 1 + dollars after t years. How much will the money be worth after t years if it is compounded n continuously (n )

8.7 The derivative of a function is defined to be lim h 0 derivative of f ( x ) = ln x + x 5 + sin x .

h 0

f[x_]= Log[x]+ x 5 + Sin[x]; Limit f[x + h] 2 f[x]+ f[x h], h 0 h2 12 + 20 x3 Sin[x] x

There are several ways derivatives can be computed in Mathematica. Each has its advantages and disadvantages, so the proper choice for a particular situation must be determined.

If f[x] represents a function, its derivative is represented by f'[x]. Higher order derivatives are represented by f''[x], f'''[x], and so on.

f[x_]= x5 + x4 + x3 + x2 + x + 1; f'[x] 1 + 2 x + 3 x2 + 4 x3 + 5 x4 f''[x] 2 + 6 x + 12 x 2 + 20 x 3 f'''[x] 6 + 24 x + 60 x 2

If a more traditional formatting of the derivatives is desired, the command TraditionalForm can be used.

f[x_]= x5 + x4 + x3 + x2 + x + 1; f'[x] // TraditionalForm 5 x4 + 4 x3 + 3 x2 + 2 x + 1 f''[x] // TraditionalForm 20 x3 + 12 x2 + 6 x + 2 f'''[x] // TraditionalForm 60 x2 + 24 x + 6

The prime notation can also be used for built-in functions, as illustrated in the next example. If the argument is omitted, Mathematica returns a pure function representing the required derivative. (Pure functions are discussed in the appendix.)

Sqrt' 1 & 2 #1 Sqrt'[x] 1 2 x Sqrt'' 1 & 4 #13/2

' Sqrt''[x]

1 4 x3/2

D[f[x], x] returns the derivative of f with respect to x. D[f[x], {x, n}] returns the nth derivative of f with respect to x.

D[x5 + x4 + x3 + x2 + x + 1, x] 1 + 2x + 3x 2 + 4x 3 + 5x 4 D[x5 + x4 + x3 + x2 + x + 1, {x, 2}] 2 + 6x + 12x 2 + 20x 3 D[x5 + x4 + x3 + x2 + x + 1, {x, 3}] 6 + 24x + 60x 2

, which can be found on the Basic Math Input palette, is equivalent to D. x will return the derivative with respect to x. The nth derivative is represented by {x, n}.

x(x5 + x4 + x3 + x2 + x + 1) 1 + 2x + 3x 2 + 4x 3 + 5x 4 {x, 2}(x5 + x4 + x3 + x2 + x + 1) 2 + 6x + 12x 2 + 20x 3 {x, 3}(x5 + x4 + x3 + x2 + x + 1) 6 + 24x + 60x 2

Derivative[n] is a functional operator that acts on a function to produce a new function, namely, its nth derivative. Derivative[n][f] gives the nth derivative of f as a pure function and Derivative[n][f][x]evaluates the nth derivative of f at x.

It is useful to remember that f' is converted to Derivative[1]. Thus, f'[x] becomes Derivative[1][x]. Higher order derivatives f'', f''', etc. are handled in a similar manner.