Use TI-84 Online for Calculus

The TI-84 graphing calculator is a must-have for calculus students. While it performs numeric (not symbolic) calculus, it's the calculator approved for AP Calculus AB/BC exams and is used in calculus classrooms nationwide.

Computing Derivatives

The TI-84 can compute the numeric derivative of a function at any given point using nDeriv(:

1. Press MATH → 8: nDeriv(
2. Enter the function, variable, and point: nDeriv(X³, X, 2)
3. Press ENTER — Result: 12 (since d/dx of x³ = 3x², and 3(2²) = 12)

You can also visualize derivatives by graphing the original function in Y₁ and nDeriv(Y₁, X, X) in Y₂ to see the derivative curve superimposed.

Computing Integrals

For definite integrals, use fnInt(:

1. Press MATH → 9: fnInt(
2. Enter: fnInt(X², X, 0, 3)
3. Press ENTER — Result: 9 (∫₀³ x² dx = x³/3 |₀³ = 9)

Graphically: You can shade the area under a curve using 2ND → CALC → 7: ∫f(x)dx, then specify the lower and upper bounds.

Exploring Limits

The TI-84 doesn't have a built-in limit function, but you can approximate limits using the TABLE feature:

1. Enter your function in Y=
2. Press 2ND → WINDOW (TABLE SETUP)
3. Set TblStart close to your limit point, ΔTbl to a small value (0.001)
4. Press 2ND → GRAPH (TABLE) to see function values approaching the limit

Example: To find lim(x→0) sin(x)/x, set TblStart = -0.01, ΔTbl = 0.001. Watch the values approach 1.

Finding Extrema (Max/Min)

1. Graph your function
2. Press 2ND → TRACE (CALC)
3. Select 3: minimum or 4: maximum
4. Set left bound, right bound, and guess — the calculator finds the exact point

Useful for Related Rates & Optimization

• Graph the function you're optimizing to visualize the solution
• Use CALC → Maximum/Minimum for optimization problems
• Store computed values in variables (A, B, C) to track multi-step solutions
• Graph both the function and its derivative side-by-side (Y₁ and Y₂)

AP Calculus Exam Tips

1. Graph a function: Y= → enter function → GRAPH
2. Find zeros of a function: 2ND → TRACE → 2: zero
3. Compute numeric derivative: MATH → 8: nDeriv(
4. Compute definite integral: MATH → 9: fnInt(

The College Board explicitly tests these four skills on the AP Calculus AB and BC exams. Master them!

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