\( \newcommand{\abs}[1]{\left| \, {#1} \, \right| } \)
17calculus
Limits Derivatives Integrals Infinite Series Parametrics Polar Coordinates Conics
Limits
Epsilon-Delta Definition
Finite Limits
One-Sided Limits
Infinite Limits
Trig Limits
Pinching Theorem
Indeterminate Forms
L'Hopitals Rule
Limits That Do Not Exist
Continuity & Discontinuities
Intermediate Value Theorem
Derivatives
Power Rule
Product Rule
Quotient Rule
Chain Rule
Trig and Inverse Trig
Implicit Differentiation
Exponentials & Logarithms
Logarithmic Differentiation
Hyperbolic Functions
Higher Order Derivatives
Differentials
Slope, Tangent, Normal...
Linear Motion
Mean Value Theorem
Graphing
1st Deriv, Critical Points
2nd Deriv, Inflection Points
Related Rates Basics
Related Rates Areas
Related Rates Distances
Related Rates Volumes
Optimization
Integrals
Definite Integrals
Integration by Substitution
Integration By Parts
Partial Fractions
Improper Integrals
Basic Trig Integration
Sine/Cosine Integration
Secant/Tangent Integration
Trig Integration Practice
Trig Substitution
Linear Motion
Area Under/Between Curves
Volume of Revolution
Arc Length
Surface Area
Work
Moments, Center of Mass
Exponential Growth/Decay
Laplace Transforms
Describing Plane Regions
Infinite Series
Divergence (nth-Term) Test
p-Series
Geometric Series
Alternating Series
Telescoping Series
Ratio Test
Limit Comparison Test
Direct Comparison Test
Integral Test
Root Test
Absolute Convergence
Conditional Convergence
Power Series
Taylor/Maclaurin Series
Radius of Convergence
Interval of Convergence
Remainder & Error Bounds
Fourier Series
Study Techniques
Choosing A Test
Sequences
Infinite Series Table
Practice Problems
Exam Preparation
Exam List
Parametrics
Parametric Curves
Parametric Surfaces
Slope & Tangent Lines
Area
Arc Length
Surface Area
Volume
Polar Coordinates
Converting
Slope & Tangent Lines
Area
Arc Length
Surface Area
Conics
Parabolas
Ellipses
Hyperbolas
Conics in Polar Form
Vectors Vector Functions Partial Derivatives/Integrals Vector Fields Laplace Transforms Tools
Vectors
Unit Vectors
Dot Product
Cross Product
Lines In 3-Space
Planes In 3-Space
Lines & Planes Applications
Angle Between Vectors
Direction Cosines/Angles
Vector Projections
Work
Triple Scalar Product
Triple Vector Product
Vector Functions
Projectile Motion
Unit Tangent Vector
Principal Unit Normal Vector
Acceleration Vector
Arc Length
Arc Length Parameter
Curvature
Vector Functions Equations
MVC Practice Exam A1
Partial Derivatives
Gradients
Directional Derivatives
Lagrange Multipliers
Tangent Plane
MVC Practice Exam A2
Partial Integrals
Describing Plane Regions
Double Integrals-Rectangular
Double Integrals-Applications
Double Integrals-Polar
Triple Integrals-Rectangular
Triple Integrals-Cylindrical
Triple Integrals-Spherical
MVC Practice Exam A3
Vector Fields
Curl
Divergence
Conservative Vector Fields
Potential Functions
Parametric Curves
Line Integrals
Green's Theorem
Parametric Surfaces
Surface Integrals
Stokes' Theorem
Divergence Theorem
MVC Practice Exam A4
Laplace Transforms
Unit Step Function
Unit Impulse Function
Square Wave
Shifting Theorems
Solve Initial Value Problems
Prepare For Calculus 1
Ready For Calculus 2?
Trig Formulas
Describing Plane Regions
Parametric Curves
Linear Algebra Review
Word Problems
Mathematical Logic
Calculus Notation
Simplifying
Practice Exams
17calculus on YouTube
More Math Help
Tutoring
Tools and Resources
Academic Integrity
Learning/Study Techniques
Math/Science Learning
Memorize To Learn
Music and Learning
Note-Taking
Motivation
Instructor or Coach?
Books
Math Books
How To Read Math Books

You CAN Ace Calculus

17calculus > exam list > calc1 exam A1

Calculus 1 - Exam A1

This is the first exam for first semester single variable calculus.

Exam Details

Tools

Time

1.5 hours

Calculators

see instructions

Questions

17

Formula Sheet(s)

none

Total Points

100

Other Tools

none

Downloads

download one page list of these questions

download multiple page exam with space to work out the solutions

Calculus 1 - Exam A1

This is the first exam for first semester single variable calculus.

Exam Details

Time

1.5 hours

Questions

17

Total Points

100

 

Tools

Calculators

see instructions

Formula Sheet(s)

none

Other Tools

none

 

Downloads

download one page list of these questions

download multiple page exam with space to work out the solutions

Instructions:
- This exam is in two main parts, labeled parts A and B, with different instructions for each part.
- Show all your work.
- For each problem, correct answers are worth 1 point. The remaining points are earned by showing calculations and giving reasoning that justify your conclusions.
- Correct notation counts (i.e. points will be taken off for incorrect notation).
- Give exact answers.

Part A - Questions 1-11

Instructions for Part A - - You have 30 minutes to complete this part of the exam. No calculators are allowed. All questions in this section are worth 3 points, except for question 10, which is worth 4 points.

Section 1

Find the indicated limit or determine that it doesn't exist.

Question 1

\(\displaystyle{ \lim_{\theta \to 0}{\left[ \frac{\sin(\theta)}{\tan(3\theta)} \right]} }\)

answer

solution

Question 2

\(\displaystyle{ \lim_{x \to 2}{\left[ \frac{x^2+x-6}{x-2} \right]} }\)

answer

solution

Question 3

\(\displaystyle{ \lim_{x \to 3}{\left[ \frac{x^2-4x+6}{x^2-9} \right]} }\)

answer

solution

Question 4

\(\displaystyle{ \lim_{x \to 1}{\left[ \frac{x-1}{x-x^3} \right]} }\)

answer

solution

Question 5

\(\displaystyle{ \lim_{x \to \infty}{\left[ \frac{5x-1}{3x^2+1/4} \right]} }\)

answer

solution

Section 2

Evaluate the following derivatives and simplify. Give all exact answers.

Question 6

\(\displaystyle{ \frac{d}{dx} \left[ (3x^2+x+1)^{2010} \right] }\)

answer

solution

Question 7

\(\displaystyle{ \frac{d}{dx}\left[ \frac{\sin^2 (x)}{\cos(x)} \right] }\)

answer

solution

Question 8

Find \( D_x y\) for \( y = \sec^2 (4x) \)

answer

solution

Question 9

Find \(f'(3)\) for \( f(x) = (2+x^2)^{4/3}\)

answer

solution

Question 10

Find \( dy/dx\) using implicit differentiation
for the curve \( 2x-y^2 = \cos(xy)+5\)

answer

solution

Question 11

Find \( D_x^{(101)} [ \cos(x) ]\)

answer

solution



Part B - Questions 12-17

Instructions for Part B - - You may use your calculator. You have one hour to complete this part of the exam. Show all your work. Correct answers are worth 1 point. The remaining points are earned by showing calculations and giving reasoning that justify your conclusions. Give exact answers.

Section 3

Solve the following problems.

Question 12

[12 points] Find the equation of the tangent line to \(\displaystyle{ y = \frac{1}{x^2+4} }\) at \( x=2\). Give your answer in slope-intercept form.

answer

solution

Question 13

[12 points] Sketch the graph of a function \(g(x)\) that satisfies the following conditions. Be sure to label your graph and axes.
(a) \(g(x)\) is continuous at \(x=1\)     (b) \(g'(1)\) does not exist
(c) \( g(1) = g(2) = 3 \)     (d) \(\displaystyle{ \lim_{x \to 2^+}{g(x)} = -\infty }\)     (e) \(\displaystyle{ \lim_{x \to \infty}{g(x)} = 1 }\)

solution

Question 14

[12 points] Identify all critical points and find the maximum and minimum value of the function
\( f(x) = x^3-3x^2+1 \) on \( S = [-1,4]\).

answer

solution

Question 15

[15 points] A ladder 3 meters long, with one end on the ground, is raised so that the angle \(\theta\) of the ladder with the ground increases by 2.5 radians per minute. Consider the right triangle formed by the ladder, the ground, and a vertical line through the top of the ladder. How fast is the area of this triangle increasing at the time when the angle \(\theta\) equals \(\pi/6\)?

answer

solution



Section 4

For the questions in this section, consider the function \( f(x) = x^4-4x^3-10 \).
[ click here to show/hide the plot ]

Question 16

[8 points] Find the intervals on which \(f(x)\) is decreasing and the intervals where \(f(x)\) is increasing.

answer

solution

Question 17

[7 points] Find the intervals on which \(f(x)\) is concave up and the intervals where \(f(x)\) is concave down.

answer

solution

Search 17Calculus

Real Time Web Analytics
menu top search
17
menu top search 17