WGU C958
CALCULUS I
Formula and Calculation Workbook
Step-by-Step Workings - Guided Practice - Independent Problems - Complete Solutions
2026 Independent Workbook
A calculation-first companion for limits, derivatives, curve analysis, optimization, related rates, antiderivatives,
definite integrals, the Fundamental Theorem of Calculus, and motion.
Academic use: Original practice material. This workbook is not an official WGU assessment and contains no reproduced Objective Assessment
questions.
,WGU C958 Calculus I - Formula and Calculation Workbook
Workbook Method
For every calculation, write four lines: formula, substitution, simplification, and interpreted answer. Do not hide algebra inside
a calculator.
Formula When to use Check
1. Identify Name the operation and relevant rule. What is being asked?
2. Set up Write the symbolic formula before numbers. Are domains and units valid?
3. Compute Show algebra one transformation at a time. Can the result be estimated?
4. Verify Differentiate, substitute, graph, or check units. Does the sign make sense?
Essential algebra reminders
Factor before canceling. Use a common denominator before adding fractions. Apply exponent and logarithm rules only to
products, quotients, and powers - never across addition. Use radians for calculus with trigonometric functions.
Self-scoring
Award 1 point each for formula, substitution, correct algebra, and final interpretation. A correct number with no
setup earns at most 2 of 4 points.
1. Limits and Continuity Calculations
Formula When to use Check
lim[x->a] f(x)=f(a) Direct substitution for continuous expressions. Denominator must not be
zero.
(x^2-a^2)=(x-a)(x+a) Factor an indeterminate 0/0 expression. Canceled factor requires x !=
a.
(sqrt(u)-sqrt(v)) conjugate Rationalize radical differences. Multiply top and bottom.
leading coefficient ratio Equal polynomial degrees at infinity. Divide by highest power.
Calculation 1: Factor and cancel
Given: lim[x->5](x^2-25)/(x-5)
1. Direct substitution gives 0/0, so factor the numerator.
2. x^2-25=(x-5)(x+5).
3. For x != 5, cancel x-5 and evaluate x+5 at 5.
Final answer
10.
Original independent practice - not affiliated with or endorsed by WGU Page 2
, WGU C958 Calculus I - Formula and Calculation Workbook
Calculation 2: Rationalize a radical
Given: lim[x->9](sqrt(x)-3)/(x-9)
1. Multiply by conjugate (sqrt(x)+3)/(sqrt(x)+3).
2. Numerator becomes x-9, which cancels with the denominator for x != 9.
3. Evaluate 1/(sqrt(x)+3) at x=9.
Final answer
1/6.
Calculation 3: Limit at infinity
Given: lim[x->infinity](8x^3-2x)/(4x^3+7)
1. Divide every term by x^3.
2. Terms 2/x^2 and 7/x^3 approach 0.
3. Take the ratio of remaining constants.
Final answer
2.
Guided practice 1
1. lim[x->4](x^2-16)/(x-4) 2. lim[x->0](sqrt(x+4)-2)/x 3. lim[x->infinity](3x^2+1)/(5x^2-x) 4. State whether (x+1)/(x^2-1) is
continuous at x=-1.
____________________________________________________________
____________________________________________________________
____________________________________________________________
____________________________________________________________
____________________________________________________________
Answers
1. 8. 2. 1/4. 3. 3/5. 4. No; the original function is undefined, although the discontinuity is removable.
2. Core Derivative Calculations
Formula When to use Check
d/dx x^n=nx^(n-1) Powers of x. Reduce exponent by one.
(cf)'=cf' Constant multiple. Keep the constant.
(f+g)'=f'+g' Term-by-term sums. Constants differentiate to zero.
y-f(a)=f'(a)(x-a) Tangent line at x=a. Use point and slope.
Original independent practice - not affiliated with or endorsed by WGU Page 3
CALCULUS I
Formula and Calculation Workbook
Step-by-Step Workings - Guided Practice - Independent Problems - Complete Solutions
2026 Independent Workbook
A calculation-first companion for limits, derivatives, curve analysis, optimization, related rates, antiderivatives,
definite integrals, the Fundamental Theorem of Calculus, and motion.
Academic use: Original practice material. This workbook is not an official WGU assessment and contains no reproduced Objective Assessment
questions.
,WGU C958 Calculus I - Formula and Calculation Workbook
Workbook Method
For every calculation, write four lines: formula, substitution, simplification, and interpreted answer. Do not hide algebra inside
a calculator.
Formula When to use Check
1. Identify Name the operation and relevant rule. What is being asked?
2. Set up Write the symbolic formula before numbers. Are domains and units valid?
3. Compute Show algebra one transformation at a time. Can the result be estimated?
4. Verify Differentiate, substitute, graph, or check units. Does the sign make sense?
Essential algebra reminders
Factor before canceling. Use a common denominator before adding fractions. Apply exponent and logarithm rules only to
products, quotients, and powers - never across addition. Use radians for calculus with trigonometric functions.
Self-scoring
Award 1 point each for formula, substitution, correct algebra, and final interpretation. A correct number with no
setup earns at most 2 of 4 points.
1. Limits and Continuity Calculations
Formula When to use Check
lim[x->a] f(x)=f(a) Direct substitution for continuous expressions. Denominator must not be
zero.
(x^2-a^2)=(x-a)(x+a) Factor an indeterminate 0/0 expression. Canceled factor requires x !=
a.
(sqrt(u)-sqrt(v)) conjugate Rationalize radical differences. Multiply top and bottom.
leading coefficient ratio Equal polynomial degrees at infinity. Divide by highest power.
Calculation 1: Factor and cancel
Given: lim[x->5](x^2-25)/(x-5)
1. Direct substitution gives 0/0, so factor the numerator.
2. x^2-25=(x-5)(x+5).
3. For x != 5, cancel x-5 and evaluate x+5 at 5.
Final answer
10.
Original independent practice - not affiliated with or endorsed by WGU Page 2
, WGU C958 Calculus I - Formula and Calculation Workbook
Calculation 2: Rationalize a radical
Given: lim[x->9](sqrt(x)-3)/(x-9)
1. Multiply by conjugate (sqrt(x)+3)/(sqrt(x)+3).
2. Numerator becomes x-9, which cancels with the denominator for x != 9.
3. Evaluate 1/(sqrt(x)+3) at x=9.
Final answer
1/6.
Calculation 3: Limit at infinity
Given: lim[x->infinity](8x^3-2x)/(4x^3+7)
1. Divide every term by x^3.
2. Terms 2/x^2 and 7/x^3 approach 0.
3. Take the ratio of remaining constants.
Final answer
2.
Guided practice 1
1. lim[x->4](x^2-16)/(x-4) 2. lim[x->0](sqrt(x+4)-2)/x 3. lim[x->infinity](3x^2+1)/(5x^2-x) 4. State whether (x+1)/(x^2-1) is
continuous at x=-1.
____________________________________________________________
____________________________________________________________
____________________________________________________________
____________________________________________________________
____________________________________________________________
Answers
1. 8. 2. 1/4. 3. 3/5. 4. No; the original function is undefined, although the discontinuity is removable.
2. Core Derivative Calculations
Formula When to use Check
d/dx x^n=nx^(n-1) Powers of x. Reduce exponent by one.
(cf)'=cf' Constant multiple. Keep the constant.
(f+g)'=f'+g' Term-by-term sums. Constants differentiate to zero.
y-f(a)=f'(a)(x-a) Tangent line at x=a. Use point and slope.
Original independent practice - not affiliated with or endorsed by WGU Page 3
