blackpenredpen Courses

Sect 3.1, Stewart Calculus 7th ed, video solutions to selected problems

Syllabus: Power rule for derivative, ex1. Power rule for derivative, ex2 (don't use quotient rule here). Power rule for derivative, ex3. Power rule for derivative, with radicals. Equation of tangent line, ex1. first and second derivative of a function, u…

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Sect 2.8, Stewart Calculus 7th ed, video solutions to select

Syllabus: definition of derivative, ex1. definition of derivative, ex2. definition of derivative, hard example. derivative of x^(2/3) by using the definition of derivative. why we need the chain rule when take derivative. Derivative of x+abs(x). sketch f…

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Sect 3.2, Stewart Calculus 7th ed, video solutions to selected problems

Syllabus: Product rule for derivative, ex1. Quotient rule for derivative, ex1. Product rule for derivative (or not?). Quotient rule for derivative, ex2. Product rule for derivative example. Quotient rule for derivative (or not?). Quotient rule for deriva…

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Sect 3.3, Derivative of Trig Functions

Syllabus: sect 3.3 #5, derivative of sec(x)*tan(x). sect 3.3 #9, derivative of x/(2-tan(x)). sect 3.3 #13, derivative of t*sin(t)/(1+t). Derivative of sin(x) and cos(x), PROOF. derivatives of tan(x) and cot(x), quotient rule, cofunction identities. deriv…

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Sect 3.4, Chain Rule

Syllabus: Chain rule for derivative. derivative of 1/(z^2+1), chain rule. derivative of cos(a^3+x^3), chain rule. derivative of x*e^(-kx), product rule and chain rule. derivative of ((x^2+1)/(x^2-1))^3. derivative of sqrt(1+2e^(3x)). derivative of 5^(-1/…

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implicit differentiation & derivative of inverse trig functions, #calculus

Syllabus: implicit differentiation y*cos(x)=x^2+y^2.derivative for e^(x/y) = x - y.implicit differentiation 4cos(x)sin(y)=1.implicit differentiation arctan(x^2*y)=x+x*y^2.Second derivative with implicit differentiation 9x^2+y^2=9.Derivative of (arctan(x)…

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logarithmic derivative, #calculus

Syllabus: Derivative of ln(1/x).derivative of log base 10 of (x^3+1), with the box.derivative of ln(x*sqrt(x^2-1)) vs. derivative of ln(x+sqrt(x^2-1)).derivative of ln((2y+1)^5/sqrt(y^2+1)).derivative of ln(ln(s)).Derivative of ln(e^-x + x*e^-x).derivati…

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Critical numbers and absolute extremes

Syllabus: Critical number of (y-1)/(y^2-y+1). Critical number of a t^(3/4)-2t^(1/4). Critical number of a x^(4/5)*(x-4)^2. Critical number of a x^2*e^(-3x). Find the critical numbers of 2cos(x)+sin^2(x). abs min and ABS MAX of ln(x^2+x+1) on [-1, 1]. abs…

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L'Hospital's Rule, #calculus

Syllabus: Q109, limit of cos(x)/(1-sin(x)). Q110, limit of (e^(2t)-1)/sin(t) as t goes to 0. limit of ln(x)/sqrt(x) as x goes to infinity, L'Hospital's Rule. limit of (8^t - 5^t)/t as t goes to 0, L'Hospital's Rule. limit of (e^x-1-x)/x^2 as x goes to 0,…

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U-Substitution, Sect 5.5, Stewart Calculus Solution, 7th ET edition

Syllabus: integral of (x+1)*sqrt(2x+x^2), calculus, u substitution. integral of e^u/(1-e^u)^2, calculus u-substitution. Integral of (lnx)^2/x, calculus u-substitution. Integral of sec^2x*tan^3x, calculus u-substitution. integral of (x^2+1)(x^3+3x)^4, cal…

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Sect2.3, Evaluating Limits Algebraically

Syllabus: Evaluate a limit by factoring and canceling. Evaluate limits by expanding the power. Evaluate limits by factoring the sum of two cubes,. Evaluate limits with square root and its conjugate. Evaluate limits with complex fractions. Evaluate limits…

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Limits at Infinities, (sect 2.6)

Syllabus: Sect 2.6, #27, limit at infinity. sect 2.6, #35, limit at infinity arctan(e^x). sect 2.6, #39, limit at infinity e^(-2x)*cos(x). checking a two-sided limit. Horizontal Asymptote, Vertical Asymptote, & Removable Discontinuity. sect 2.6, #51. sec…

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Sect 2.7, Definition of Derivative

Syllabus: Definition of derivative in terms of a limit, (def 1). Definition of derivative in terms of a limit, (def 2). derivative of x^-2 with the definition of derivative. definition of the derivative with square root (and conjugate). sect 2.7 #13. di…

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Calculus: Sect 5.3, FTC1 and FTC2, Stewart Calculus Solution, 7th ET edition

Syllabus: Fundamental theorem of calculus (part 1) example#1. Fundamental theorem of calculus (part 1) example#2. Integral of x^3-2x from -1 to 2. Integral of sqrt(x) from 1 to 9. Integral of (u+2)(u-3) from 0 to 1. Integral of (x-1)/sqrt(x) from 1 to 9.…

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Calculus Sect 7.1, Integration by Parts

Syllabus: Integration by Parts (udv format) Calculus 2. Integrals with both u-substitution & integration by parts (DI method). Integral of tan^-1(x), integral of ln(x)/x^2, integral of e^(3x)*sin(2x), integration by parts. integration by parts, DI method…

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• 3-4 hours worth of material
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