Numeric calculus and sums

20.1The MATH menu tools#

These tools work on an expression you type, so you do not need to graph anything. Each takes the expression first, then the variable, then the numbers it needs, and a closing bracket.

Item	Syntax	Gives
6	fMin(expression, variable, lower, upper)	The x where the expression is lowest.
7	fMax(expression, variable, lower, upper)	The x where the expression is highest.
8	nDeriv(expression, variable, value)	The slope at the value.
9	fnInt(expression, variable, lower, upper)	The definite integral.
0	Σ(expression, variable, start, end)	The sum of the expression as the variable runs from start to end.

20.2Find the minimum or maximum of an expression#

Example 20.1

Minimum of x² − 2x

$$\min_{-5\le x\le5}(x^2-2x)\ \text{at}\ x=1$$

1. Press math then 6 (fMin() and type X²−2X,X,−5,5).

   math6X,T,θ,nx²−2X,T,θ,n,X,T,θ,n,(−)5,5)enter

Example 20.2

Maximum of −x² + 4x

$$\max_{0\le x\le5}(-x^2+4x)\ \text{at}\ x=2$$

1. Press math then 7 (fMax() and type −X²+4X,X,0,5.

   math7(−)X,T,θ,nx²+4X,T,θ,n,X,T,θ,n,0,5)enter

20.3Find a derivative at a point (nDeriv)#

$$\operatorname{nDeriv}(f(x),x,a)\approx\frac{f(a+h)-f(a-h)}{2h}$$

Example 20.3

Slope of x² at x = 3

$$\frac{d}{dx}x^{2}\Big|_{x=3}=6$$

1. Press math then 8 and type X²,X,3.

   math8X,T,θ,nx²,X,T,θ,n,3)enter

20.4Find a definite integral (fnInt)#

Example 20.4

Integral of x² from 0 to 1

$$\int_{0}^{1}x^{2}\,dx=\frac13$$

1. Press math then 9 and type X²,X,0,1.

   math9X,T,θ,nx²,X,T,θ,n,0,1)enter

Example 20.5

Integral of sin x from 0 to π

$$\int_{0}^{\pi}\sin x\,dx=2$$

1. Use radian mode and type sin(X),X,0,π.

   math9sinX,T,θ,n),X,T,θ,n,0,2ndπ^)enter

20.5Add up a series (summation)#

$$\sum_{K=1}^{10}K^{2}=385$$

Example 20.6

Sum of the first ten squares

1. Press math then 0 (the Σ( item) and type K²,K,1,10.

   math0alphaK(x²,alphaK(,1,10)enter

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