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# Class Notes for Mathematics at University of Ottawa (page 4)

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##### MAT 1300 Lecture Notes - Lecture 6: Product Rule 24HRPremium

MAT1300 LECTURE 6 CHAIN RULE CONTINUATION OF LECTURE 5 f(x) = |x| what is f(0.00001) ? answer =1 DEFINITION Let f be a function the line tangent to the graph of f at (a, f(a)) is the line passing through (a, f(a)) ...

Mathematics
MAT 1300
Hung-Chang Liao
##### MAT 1339 Lecture Notes - Fall 2018 Lecture 5 - Power rule 24HRPremium

MAT1339 - Lecture 5 - Limits and derivatives Infinite limits: The 4 possibilities of 1- 2- 3- + ...

Mathematics
MAT 1339
Michael Reeks
##### MAT 1300 Lecture 5: MAT 1300 –LECTURE 5 – RULES 24HRPremium

6) ddx (lnx) =1x EXAMPLES Find the derivatives a) f(x) =3x +2x+3 =6x +2 b) g(x)= 3 sqrt(x) +4x 12 1 = 3x + 4x =3 (12 x12)+ 4 (1 x ) 12 2 =(32) x 4x c) h(x) = ddx (ln(x )) = ddx 2 (lnx) = 2 (ddx (lnx) = 2 . 1x PRODUCT AND ...

Mathematics
MAT 1300
Hung-Chang Liao
##### MAT 1339 Lecture 4: MAT1339 – Lecture 4 - Limits and Instantaneous rate of change 24HRPremium

MAT1339 Lecture 4 Limits and Instantaneous rate of change Absolute value in limits: You need to cancel a common factor to get the limit and solve inequalities Example: Sidenote: The limit in a absolute value function exis...

Mathematics
MAT 1339
Michael Reeks
##### MAT 1300 Lecture 4: MAT 1300 LECTURE 4 –LIMITS and continuity 24HRPremium

Then f(1) = 2 But when x approaches 1 the value f(x) approaches 1 If f(x) approaches the number L when x approaches C from both sides ( but not equal to C ) we write: Lim f(x) = L XC diagram by teacher...

Mathematics
MAT 1300
Hung-Chang Liao
##### MAT 1320 Lecture 3: Tangents, Limits and Limit Laws 24HRPremium

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Mathematics
MAT 1320
Michael Newman
##### MAT 1300 Lecture Notes - Lecture 3: Logarithm, Asymptote 24HRPremium

An exponential function has the form f(x)= ab (b>0)x - In both cases y=0 is a horizontal asymptote x - Domain of b is (- infinity...

Mathematics
MAT 1300
Hung-Chang Liao
##### MAT 1339 Lecture Notes - Lecture 3: Indeterminate Form 24HRPremium

MAT1339 Lecture 3 Limits Slope of lines: You can use any point because these slopes are constant. Slope of secant lines or average rate of change: These slopes arent constant and rely on a,b to be determined. Slope of tang...

Mathematics
MAT 1339
Michael Reeks
##### MAT 1320 Lecture 2: Modifying, Composition and Exponential Functions 24HRPremium

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Mathematics
MAT 1320
Michael Newman
##### MAT 1339 Lecture 2: MAT1339-Lecture2 Secant lines & Rate of change 24HRPremium

MAT1339 Lecture 2 Secant lines Average rate of change Secant line: A straight line that intersects at 2 points on a function. It comes from the word secare, which means to cut. The secant of a function is equal to the ave...

Mathematics
MAT 1339
Michael Reeks
##### MAT 1300 Lecture Notes - Lecture 2: Asymptote, Coefficient, Graphing Calculator 24HRPremium

QUADRATICS Standard form: 2 F(x)= ax +bx+c Graph opens up if a>0 QUADRATICS Standard form: 2 F(x)= ax +bx+c Graph opens up if a>0hence x= -2 or x=-3 QUADRATIC FO...

Mathematics
MAT 1300
Hung-Chang Liao
##### MAT 1300 Lecture Notes - Lecture 1: Negative Number 24HRPremium

THIS IS A FUNCTION INPUT OUTPUT 1 1 3 4 3 9 THIS IS NOT A FUNCTION (input 3 has two different outputs) Example1 2 f(x)= x +2 ...

Mathematics
MAT 1300
Hung-Chang Liao
##### MAT 1300 Lecture Notes - Lecture 8: Maxima And Minima, Implicit Function 24HRPremium

MAT1300F- Lecture #8- Derivatives Part 2 *Note: go over the exam review that is now posted on Brightspace Learning goals for this lesson: 1. Chain rule 2. Implicit differentiation 3. Maximum and Minimums 4. Short ex...

Mathematics
MAT 1300
Dongyang Kuang
##### MAT 1300 Lecture Notes - Lecture 7: Product Rule, Inflection, Power Rule 24HRPremium

MAT1300F- Lecture #7- Derivatives Part 2 Learning goals for this lesson: 1. Understand the chain rule 2. Introduction to implicit differentiation Recap of derivatives F(x) original function F (x) the first deriva...

Mathematics
MAT 1300
Dongyang Kuang
##### MAT 1300 Lecture Notes - Lecture 1: Category 3 Cable, Cube Root, Square Root 24HRPremium

MAT1300F-Lecture 1- Recap of Calculus The point of this course is basic calculus geared toward economic applications. Definitions 1. Function- A function is a rule for a relationship between an input, or independe...

Mathematics
MAT 1300
Dongyang Kuang
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