Common Errors & Fixes

This page covers the most common errors students encounter in Math 119, with copy-paste solutions.

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R Errors

“Error: object ‘f’ not found”

What it means: You’re trying to use a function that hasn’t been defined yet.

Fix: Define the function before using it.

Show Fix 
# BAD: Using f before defining it
uniroot(f, c(0, 5))$root

# GOOD: Define f first
f <- function(x){ 3*x - 5 - exp(-x) }
uniroot(f, c(0, 5))$root

“Error: f() values at end points not of opposite sign”

What it means: Your interval [a,b] for uniroot() doesn’t contain a zero. The function has the same sign at both endpoints.

Fix: Plot the function first to find an interval where it crosses zero.

Show Fix 
# Define your function
f <- function(x){ 3*x - 5 - exp(-x) }

# Plot to see where f(x) crosses zero
x <- seq(-5, 10, 0.1)
plot(x, f(x), type="l")
abline(h=0, col="red")  # Red line at y=0

# Now pick an interval where the curve crosses the red line
# From the plot, looks like it crosses between 0 and 5
uniroot(f, c(0, 5))$root

Common mistake: Picking the interval before looking at the plot.

“Error: unexpected ‘}’ in …”

What it means: Mismatched curly braces - you have a closing } without a matching opening {, or vice versa.

Fix: Count your braces. Every { needs a matching }.

Show Fix 
# BAD: Missing opening brace
f <- function(x) 3*x - 5 }

# GOOD: Matching braces
f <- function(x){ 3*x - 5 }

# BAD: Extra closing brace
f <- function(x){ 3*x - 5 }}

# GOOD: One opening, one closing
f <- function(x){ 3*x - 5 }

“Error in exp(x) : non-numeric argument”

What it means: You’re passing something that’s not a number to a math function.

Fix: Check that x is actually a number or numeric vector.

Show Fix 
# BAD: x is undefined
f <- function(x){ exp(x) }
f()  # Error: missing argument

# GOOD: Pass a number
f(2)

# BAD: Passing text
f("hello")  # Error

# GOOD: Pass numbers
f(2)
f(seq(0, 5, 0.1))  # Vector of numbers

“Warning: NaNs produced”

What it means: You’re computing something undefined, like \(\sqrt{-1}\) or \(\log(-5)\).

Fix: Check domain restrictions. Often happens with square roots of negative numbers or logs of non-positive numbers.

Show Fix 
# Example: log() requires positive numbers
f <- function(x){ log(3*x - 2) }

# This will produce NaN for x < 2/3
f(0)  # log(3*0 - 2) = log(-2) → NaN

# Check domain: Need 3*x - 2 > 0, so x > 2/3
f(1)  # log(3*1 - 2) = log(1) = 0 ✓

Common mistake: Forgetting that \(\ln(x)\) requires \(x > 0\).

“Error: could not find function ‘uniroot’”

What it means: You’re using a function from a package that isn’t loaded.

Fix: Actually, uniroot() is built-in - this error means you misspelled it.

Show Fix 
# BAD: Misspelled
uniRoot(f, c(0, 5))  # Error

# GOOD: Correct spelling (lowercase 'r')
uniroot(f, c(0, 5))

Mathematica Errors

“Syntax: … cannot be followed by …”

What it means: Wrong bracket type or missing operator.

Fix: Use [] for functions, {} for lists, () for grouping.

Show Fix 
(* BAD: Using () instead of [] for function *)
Integrate(x^2, {x, 0, 5})  (* Error *)

(* GOOD: Use [] for functions *)
Integrate[x^2, {x, 0, 5}]

(* BAD: Missing * for multiplication *)
Integrate[2x, {x, 0, 5}]  (* Error *)

(* GOOD: Use * explicitly *)
Integrate[2*x, {x, 0, 5}]

“Part specification is longer than depth of object”

What it means: You’re trying to access a part of the result that doesn’t exist.

Fix: Check what your function returned. Use //FullForm to see the structure.

Show Fix 
(* If Solve returns an empty set *)
result = Solve[x^2 == -1, x, Reals]
(* Returns {} because no real solution *)

(* Accessing result[[1]] will error *)

(* Check first if result is non-empty *)
If[Length[result] > 0, result[[1]], "No solution"]

“NIntegrate failed to converge”

What it means: The numerical integration is having trouble. Often happens with infinite limits or poorly behaved functions.

Fix: Increase precision or check your integrand.

Show Fix 
(* If standard NIntegrate fails *)
NIntegrate[1/Sqrt[50*Pi]*Exp[-(1/50)*(x-21)^2], {x, -Infinity, 22}]

(* Try increasing WorkingPrecision *)
NIntegrate[1/Sqrt[50*Pi]*Exp[-(1/50)*(x-21)^2],
           {x, -Infinity, 22},
           WorkingPrecision -> 20]

“Set::setraw: Cannot assign to raw object”

What it means: You used = instead of == in an equation.

Fix: Use == for equations, = for assignment.

Show Fix 
(* BAD: Using = in equation *)
Solve[x^2 = 4, x]  (* Error *)

(* GOOD: Use == for equations *)
Solve[x^2 == 4, x]

(* Note: = is for assignment *)
myVar = 5  (* This assigns 5 to myVar *)

Math/Algebra Errors

Forgetting Chain Rule

Symptom: Derivative is wrong by a factor.

Fix: Check if you have a composition of functions. If so, multiply by the inner derivative.

Show Fix

Problem: Find \(\frac{d}{dx}[(3x^2 + 1)^5]\)

BAD: Just using power rule
= 5(3x^2 + 1)^4  ❌ Missing inner derivative!

GOOD: Chain rule
Outer: f(u) = u^5 → f'(u) = 5u^4
Inner: u = 3x^2 + 1 → u' = 6x
Result: 5(3x^2 + 1)^4 · 6x = 30x(3x^2 + 1)^4 ✓

Common mistake: Forgetting to multiply by the derivative of what’s inside the parentheses.

Sign Errors in Derivatives

Symptom: Answer is correct except for a negative sign.

Fix: Carefully track negative signs through each rule.

Show Fix

Problem: Find \(\frac{d}{dx}[e^{-2x}]\)

Chain rule:
Outer: f(u) = e^u → f'(u) = e^u
Inner: u = -2x → u' = -2  ← Don't forget this negative!
Result: e^{-2x} · (-2) = -2e^{-2x} ✓

Common mistake: Forgetting that the derivative of \(-2x\) is \(-2\), not \(2\).

Domain Restrictions

Symptom: Getting undefined or NaN results.

Fix: Check domain restrictions before solving.

Show Fix

Problem: Solve \(\ln(3x - 2) = 5\)

BEFORE solving, check domain:
ln(3x - 2) requires 3x - 2 > 0
So x > 2/3

Then solve:
3x - 2 = e^5
3x = e^5 + 2
x = (e^5 + 2)/3 ≈ 50.06 ✓ (This is > 2/3, so valid)

Common mistake: Solving first, then checking domain. Check domain BEFORE solving to avoid invalid solutions.

Wrong k in PDF Normalization

Symptom: All subsequent probability calculations are wrong.

Fix: Always verify \(\int f(x) \, dx = 1\) after finding \(k\).

Show Fix

Problem: Find \(k\) for \(f(x) = k(15-x)\) on \([0, 15]\)

Set up: ∫₀¹⁵ k(15-x) dx = 1

Compute: k[15x - x²/2]₀¹⁵ = k(225 - 112.5) = 112.5k = 1

Solve: k = 1/112.5 = 2/225

VERIFY: ∫₀¹⁵ (2/225)(15-x) dx
       = (2/225)[15x - x²/2]₀¹⁵
       = (2/225)(112.5)
       = 1 ✓

Common mistake: Finding \(k\) but not verifying it. Wrong \(k\) makes E[X], Var(X), and all probabilities wrong.

Conceptual Errors

Confusing Maximum vs Minimum

Symptom: Getting a minimum when you expected a maximum (or vice versa).

Fix: Use the second derivative test to classify critical points.

Show Fix

At a critical point where \(f'(c) = 0\):

  • If \(f''(c) > 0\) → concave up → local minimum (like a valley ∪)
  • If \(f''(c) < 0\) → concave down → local maximum (like a hill ∩)

Example: Optimization problem gives \(a_1 = 0.0005253\)

# Find second derivative
f_second <- function(a1){ -328767530 }
f_second(0.0005253)
# Returns: -328767530 (negative!)

# Negative → concave down → MAXIMUM ✓

Memory trick: - Positive 2nd derivative → smiley face ∪ → minimum - Negative 2nd derivative → frowny face ∩ → maximum

Percentile Direction Confusion

Symptom: Trying to find score from percentile, but using percentile-from-score formula (or vice versa).

Fix: Identify what you know and what you’re finding.

Show Fix

Two types of problems:

Type 1: Score → Percentile (you KNOW the score, FIND the percentile)

(* Given: Student scored 22 on ACT *)
(* Find: What percentile? *)
NIntegrate[f[x], {x, -Infinity, 22}]  (* Integrate UP TO the score *)
(* Returns: 0.54 = 54th percentile *)

Type 2: Percentile → Score (you KNOW the percentile, FIND the score)

(* Given: Student is at 80th percentile *)
(* Find: What score? *)
NSolve[NIntegrate[f[x], {x, -Infinity, xp}] == 0.80, xp]
(* Returns: xp ≈ 25.2 *)

Common mistake: Using the wrong direction - check whether you’re given the score or the percentile!

Getting Help

If your error isn’t listed here:

  1. Copy the exact error message and search it online
  2. Check your syntax against the Quick Reference
  3. Ask on Canvas discussion board with:
    • The error message
    • Your code (copy-paste, not screenshot)
    • What you expected to happen
  4. Office hours - bring your code and error