DIAGNOSTIC TEST CALCULUS 2 MATH 208.

Slides:

Advertisements

Similar presentations

Ff. Directions: 1.Click on the picture that begins with Ff. 2.The pictures are linked to a slide that will tell you if you got it correct or you need.

Advertisements

Integration Using Trigonometric Substitution Brought to you by Tutorial Services – The Math Center.

Example Express -8sinx° + 15cosx° in the form ksin(x + )° *********

Trig Graphs. y = sin x y = cos x y = tan x y = sin x + 2.

Example: Obtain the Maclaurin’s expansion for

2 step problems 5) Solve 0.5Cos(x) + 3 = 2.6 1) Solve 4Sin(x) = 2.6 2) Solve Cos(x) + 3 = ) Solve 2Tan(x) + 2 = ) Solve 2 + Sin(x) =

6.2 Trigonometric Integrals. How to integrate powers of sinx and cosx (i) If the power of cos x is odd, save one cosine factor and use cos 2 x = 1 - sin.

Find the period of the function y = 4 sin x

6.5.3 – Other Properties of Inverse Functions. Just like other functions, we need to consider the domain and range of inverse trig functions To help us.

START Help Pac-Man find his dinner by answering math questions correctly. Try to go as fast as you can. You can do it! Click the Pac Man to begin playing.

Multiple Angle Formulas ES: Demonstrating understanding of concepts Warm-Up: Use a sum formula to rewrite sin(2x) in terms of just sin(x) & cos(x). Do.

Clicker Question 1 What is the derivative of f(x) = 7x 4 + e x sin(x)? – A. 28x 3 + e x cos(x) – B. 28x 3 – e x cos(x) – C. 28x 3 + e x (cos(x) + sin(x))

Tips For Learning Trig Rules. Reciprocal Rules Learn:

If is measured in radian Then: If is measured in radian Then: and: -

The Antiderivative Safa Faidi. The definition of an Antiderivative A function F is called the antiderivative of f on an interval I if F’(x) =f(x) for.

Precalculus Section 7.5. Warmup Graph the function. State the Domain, Range, Asymptotes, and Period 1.f(x) = -2 tan(1/3 x) 2.f(x) = sec(2x) + 1.

B1.6 – Derivatives of Inverse Trig Functions

 Content  What is derivation?  Derivation of trigonometry function  Derivation’s rules.

Quiz Name Here Click to start Question 1 Type question here Wrong Answer Right Answer.

Test Your Knowledge. x + 3 =6 a.5 b.4 c.3 d.2 y - 11= 78 a. 69 b. 89 c. 87 d. 68.

2.4 The Chain Rule Remember the composition of two functions? The chain rule is used when you have the composition of two functions.

MONEY! Pick the correct coin! Click here to get started!!

Using our work from the last few weeks,

Trig Functions Ms. Roque 11 th Grade Trigonometry Course Next slide.

Trigonometry Review Find sin(  /4) = cos(  /4) = tan(  /4) = Find sin(  /4) = cos(  /4) = tan(  /4) = csc(  /4) = sec(  /4) = cot(  /4) = csc(

THE MAGIC OF SUBTRACTION 2009 Quinín Freire 1 LEARNING.

Lesson 3-5 Chain Rule or U-Substitutions. Objectives Use the chain rule to find derivatives of complex functions.

Solving Trig Equations Starter CStarter C Starter C SolutionsStarter C Solutions Starter DStarter D Starter D SolutionsStarter D Solutions.

12/20/2015 Math 2 Honors - Santowski 1 Lesson 53 – Solving Trigonometric Equations Math 2 Honors - Santowski.

Practice Evaluate each of the following.

Some needed trig identities: Trig Derivatives Graph y 1 = sin x and y 2 = nderiv (sin x) What do you notice?

Mr S Paine Year 7. Which is the correct line of symmetry? This one? (Click here) This one? (Click here)

Lines of Symmetry Quiz. Time to test if you understand lines of symmetry!! In this Quiz you will have questions and underneath you will have 3 choices.

Quiz Name Here Click to start Question 1 Type question here Wrong Answer Right Answer.

“Click for Instruction “Click here to play.” If you select the correct answer, you will continue to the next question. If you the wrong answer, you will.

Dean Bates P derivatives of trig functions.

Trigonometry Review Find sin(  /4) = cos(  /4) = tan(  /4) = Find sin(  /4) = cos(  /4) = tan(  /4) = csc(  /4) = sec(  /4) = cot(  /4) = csc(

Multiplication Level 1 (Facts 0-2) Read These Instructions:  Try to get the answer before the computer puts it on the screen.  Do not click on your.

4.1 Linear Approximations Fri Oct 16 Do Now Find the equation of the tangent line of each function at 1) Y = sinx 2) Y = cosx.

Trigonometry Review Find sin(  /4) = cos(  /4) = tan(  /4) = Find sin(  /4) = cos(  /4) = tan(  /4) = csc(  /4) = sec(  /4) = cot(  /4) = csc(

Power Rule is a corallary to Chain Rule. Power Rule If f(x) = x n then f ' (x) = n x (n-1) Replacing x by g(x) gives.

Clicker Question 1 What is  x sin(3x) dx ? – A. (1/3)cos(3x) + C – B. (-1/3)x cos(3x) + (1/9)sin(3x) + C – C. -x cos(3x) + sin(3x) + C – D. -3x cos(3x)

3.5: Derivatives of Trig Functions Objective: Students will be able to find and apply the derivative of a trigonometric function.

Sin x = Solve for 0° ≤ x ≤ 720°

Clicker Question 1 What is  cos 3 (x) dx ? – A. ¼ cos 4 (x) + C – B. -3cos 2 (x) sin(x) + C – C. x – (1/3) sin 3 (x) + C – D. sin(x) – (1/3) sin 3 (x)

Trigonometric Identity Review. Trigonometry Identities Reciprocal Identities sin θ = cos θ = tan θ = Quotient Identities Tan θ = cot θ =

CHAPTER Continuity Fundamental Theorem of Calculus In this lecture you will learn the most important relation between derivatives and areas (definite.

Division Level 1 (facts 0-2, 5, 9) © Thomas 2002.

Division Level 2 (facts 0-9) © Thomas 2002 Click here to start program.

sinx + circle 90 o 180 o  0o0o 270 o 1 The Trigonometric Ratios for any angle

Jeopardy Simplify Trig expressions Verify Trig Identities Find all Solutions Solutions with multiple angles Solutions with factoring Q $100 Q $200 Q $300.

Math 1304 Calculus I 3.2 – Derivatives of Trigonometric Functions.

1 Lecture 7 of 12 Inverse Trigonometric Functions.

Chapter 10 – Trigonometric (Functions) Q1

The Fundamental Theorem of Calculus

MATH 1330 Section 6.3.

MATH 1330 Section 6.3.

MATH 1330 Review for Exam 3.

C4 Integration.

Review 5.1 to 5.3.

Finding a Limit as x c Plug in---Factor/Conjugate.

1 step solns A Home End 1) Solve Sin(x) = 0.24

Last time… Homework questions?.

Clicker Question 1 What is x sin(3x) dx ? A. (1/3)cos(3x) + C

மீன்’ பிடிப்போம்’.

MATH 1330 Section 6.3.

3 step problems Home End 1) Solve 2Sin(x + 25) = 1.5

Half-Angle Identities

Quiz Name Here Click to start.

Quiz Name Here Click to start.

Presentation transcript:

DIAGNOSTIC TEST CALCULUS 2 MATH 208

1. The derivative of f(x) = x cosx is 1 sin x cos x + x sin x cos x - x sin x -1 sinx

Wrong! The derivative of uv is (uv)’ = u’v+uv’ NOT u’v’ Click here to continue Click here to try again

Wrong! The derivative of cos x is – sin x, not sin x Click here to continue Click here to try again

Correct! Great job!

2. The derivative of f(x) = is

Wrong! The derivative of is Click here to continue Click here to try again

Correct! Great job!

3. The derivative of f(x) = sin3x is 3 sin x cos x -3 sin2x cos x 3 sin2x cos x 3 sin2 x

Wrong! The derivative of un is (un)’ = nun-1u’ and The derivative of sin x is cos x, not – cos x Click here to continue Click here to try again

Correct! Great job!

4. An antiderivative of x2+ sec2 x is 2x + 2sec2x tan x x3/3 + tan x x3/3 - tan x

Wrong! The derivative of x2 is 2x, the antiderivative is x3/3 The antiderivative of sec2x is tanx Click here to continue Click here to try again

Correct! Great job!

5. The integral (x5 – cos 2x)dx is 5x4 - 2sin 2x x5/5 + (sin 2x)/2 x5/5 – 2 sin 2x x5/5 – (sin 2x)/2

Wrong! The derivative of x5 is 5x4, the antiderivative is x5/5 The antiderivative of cos nx is (sin nx)/n Click here to continue Click here to try again

Correct! Great job!

CONGRATULATION! YOU ARE DONE!