Portfolio Entry

Portfolio Entry

MCV4UW • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Ariel Chan

*Corrections are on grided paper

U1

Limits & Continuity

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Page 1Question 1 a

Without using your graphing calculator, show that there is a root of the equation x³ + x² - x - 2 = 0 between 1 and 2. Provide appropriate justification.

+ Course expectations Met

Page 3Question 4 e

Determine each limit, whether finite or infinite. If the limit does not exist, A PRECISE EXPLANATION is required. If it exists, clearly demonstrate why.

+ Course expectations Met

Page 3Question 4 f

Determine each limit, whether finite or infinite. If the limit does not exist, A PRECISE EXPLANATION is required. If it exists, clearly demonstrate why.

+ Course expectations met

Page 3Question 4 g

Determine each limit, whether finite or infinite. If the limit does not exist, A PRECISE EXPLANATION is required. If it exists, clearly demonstrate why.

+ Course expectations met

Page 4 Question 7

Determine whether the statement is true or false. If it is true, explain why. If it is false, clearly explain why it is false or give an example that disproves the statement: If f is continuous at 5 and f(5) = 2 and f(2) = 3, then lim x → 2 [f(4x²-11)] = 2.

+ Course expectations met

U2

Derivatives

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Page 1Question 1

Determine lim sin(5θ) θ→0 sin(2θ) Show all steps as demonstrated in class to justify your answer.

+ Course expectations Met

Page 2Question 4

Is the function h(x) differentiable at x=2? Justify your answer as demonstrated in class.

+ Course expectations met

Page 2Question 6

if f(x)=x^n where n is a whole number, then f^(n+1) = ?

+ Course expectations met

Page 3Question 9

Find the equation of the tangent line, in standard form, to the curve f(x) = sinx • cos²x at (π/4, 1/2√2). Draw any special triangles used in your calculations.

+ Course expectations Met

Page 5 Question 14 c

Differentiate. DO NOT re-write the original function befopre differentiating. Express final answers in factored form with positive exponents.

+ Course expectations Met

U3

Implicit Differentiation & Related Rates

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Page 1Question 1

Given f(x) = 2x+3 , find f''(x). 4x-5

+ Course expectations Met

Page 5Question 7

The radius of a cylinder decreases at a rate of 0.5 cm/min. At a specific instant the radius and height of the cylinder are 5 cm and 20 cm respectively. What should the rate of change in height be so that the volume remains constant? Neither a diagram nor let statements are required.

+ Course expectations Met

U4

Derivatives of Exp., Log. & Inverse Trig. Functions

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Page 1 Question 3

Sketch y=tan^-1(x). Plot 5 points accurately. Label the scale on both axes. Then, state the domain and range.

+ Course expectations met

Page 3 Question 6

a, c & d

Determine each limit. Show all your work. you will not be able to apple l'Hopital's Rule in all cases. If you use l'Hopital's Rule, you must indicate each use by writing the letter H above the equal sign of the appropriate step(s).

In question 6 a, 6 c and 6 d, I made a simular mistake with the l'Hopital's Rule . . .

+ Course expectations met

Question 6 Corrected Solutions

Part a

Part d

Part c

Page 4Question 7 d

Differentiate and simplify. Express final answers with positive exponents. Write final answer as a single fraction where necessary.

+ Course expectations Met

Page 5Question 8

Differentiate y = log₂x 2^xExpress final answer using natural logarithms only.

+ Course expectations Met

Page 5Question 9

Given y = (x²-1)⁴ √(x-1)Show that dy = (15x-1) / [ 2(x+1)(x-1) ] dx

+ Course expectations Met