Dawnbridge

TI-Nspire CX II field manual for IB Math

Everyone · 20 of 45

20

Solving an equation numerically

All courses

Type an equation in as it is written and let the calculator solve it. The TI-84 and Nspire return one root chosen by your starting guess, so a second pass is needed for a second root; the Casio returns the whole list.

Goal

Solve ​ex=5x​ for all real ​x.

1

Open the Calculate scratchpad with , then → Algebra → Numerical Solve. That pastes nSolve( onto the entry line, ready for the equation.

2

Type the equation as it is written, including the equals sign: inserts ​ex, then . There is no rearranging into ​f(x)=0​ first.

3

Add the starting guess. Press then , close with , and press . The full call reads nSolve(e^x=5x,x=0). That second argument is not optional decoration: it is what decides which root comes back.

f(x) =ex
g(x) =5⋅x
Solve f(x) = g(x)
Scratchpad
RAD
nSolve(ex=5⋅x,x=0.)
0.259171
4

It returned one root, not all of them. nSolve works outward from the guess and stops at the first root it finds, so the answer depends on where you started. Graphing the two sides shows they cross twice, so a guess of ​0​ has only found the left-hand crossing.

5

Recall the line with , change the guess to ​3, and press again. Starting near the second crossing sends nSolve to that one instead.

f(x) =ex
g(x) =5⋅x
Solve f(x) = g(x)
Scratchpad
RAD
nSolve(ex=5⋅x,x=3.)
2.54264
Result

​x=0.259​ and ​x=2.54​ to 3 s.f. Always graph the equation as well, so you know how many roots you are looking for before you trust a single nSolve answer.

Your turn

Work each one on your calculator, then check the answer.

  1. 1

    Solve ​lnx=x−2.

  2. 2

    Solve ​x3=2x.

  3. 3

    Solve ​cosx=x2−1, working in radians.