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Limit x →1 (1 - x^(-1/7))/(1 - x^(-4/7)) = ? Solve WITHOUT using L' Hôpital's Rule.
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#short #limit #algebra
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Following are some of playlist and ideos on calculus, algebra, logarithm, trigonometry and some older video on ioT/Smart Home:
MIT Integration Bee
Area Under Curves
JEE-Main, India
UK AQA/CIE A-Level
Stanford Math Tournament
Calculus
[1] Solving Gaussian Integral (integration of gaussian function) by Feynman’s Method.
[2] Created another 1 minute video for Happy π day! Solve an integral and the answer is π!
[3] Solving integral x^(9)*(x^(10) + 1)/(x^(20) + 1) dx. Can we solve it using substitution?
[4] Solving integral 1/(-sqrt(x^2 + 4*x + 3)) dx. Can it be solved by substitution?
[5] Solving sum of k=0 to ∞ for integral sin^(2k) (x) dx. Solution is much easier than expected!
[6] Solving area of region bounded between 2 curves, i.e., {(x,y): x^2 ≤ y ≤ x + 2} using integration.
[7] Solving integral (x^2 - 1)/(x^4 - 1) dx.
[8] Given y=kx^2, x=ky^2, k is +ve constant & area enclosed between parabola curves is 1 unit^2. Find k.
[9] Given f(x) = integral (x^5-16x)/(x^8-256) dx and f(-2) = π/32. Find f(2). Explanation in 60 seconds
Algebra
[1] Is this a quartic or quadratic problem? Can we solve it within 60 seconds and without calculator?
[2] Solving (10016*104*12*8 + 256)^0.5 but without using calculator & computer. Answer is a nice number!
[4] 15 seconds video on solving sqrt(10300 - 9*10*10*11) without using calculator and computer.
[5] Given x^2 - x - 1 = 0, solve cos^1 ((3/2)*(7*x + 1)/(x^9 - 18*x - 13)).
[6] An infinite radical equation, i.e., sqrt(3*sqrt(7*sqrt(…))) solve by Geometric Series.
[7] If (√ 2 + √ 3)^11 = a √ 2 + b√ 3, then (a² - (3/2)*b²)^11 = ?
[8] Given (|x-3| - 4)^2 = 4. How many answers for x?
Logarithm/exponential
[1] Solving a finite power equation of (ln(x))^2. The solution is surprisingly easier than expected.
[2] Given that ln(3) is approximately equal to 1.099, find ln(3.1) using calculus without calculator.
[3] Solving x^(ln x) = x for real numbers. How many answers for x?
[4] Solving a radical-absolute equation. Is this a quadratic equation too?
[5] Solving a logarithm-quadratic question of Stanford Math Tournament 2021. Calculator is not allowed.
[6] 15 seconds video to explain the answer for ln(-1) based on principal value of trigonometry.
[7] 15 seconds video on solving x^(ln|x|) = 1/|x|. There are 4 answers for x?
Trigonometry
[1] Solving a trigonometry-power equation? Solution is fairly simple and can be explained in 60 seconds.
[2] 45 seconds video deriving cos(-θ)=cos(θ) & sin(-θ)=-sin(θ). Basic identities of trigonometry Part 5.
[3] 15 seconds video for deriving sec^2(x) = tan^2(x) + 1. Basic identities of trigonometry Part 1.
[4] 15 seconds video for deriving sin^2(x) + cos^2(x) = 1. Basic identities of trigonometry Part 2.
IoT/Smart Home
[1] Smart Home: Control Autogate using Sonoff RF Bridge with eWelink App & voice command of Amazon Alexa
[2] Can We Remote Access Node-red Server from another computer? Part 1: Wireless/Wire LAN
[3] How to install Amazon Alexa App on iPhone in Malaysia or region without it in Apple Store (Feb 2021)
[4] Smart Home: Security Automation Alarm System using Aqara G2H Camera Hub, Motion & Contact Sensors
[5] Node-red Iot Server & Telegram bot - Part 2: Search & display photo using telegrambot (Windows 10)
Thanks for watching my video. Please subscribe to my channel.
Following are some of playlist and ideos on calculus, algebra, logarithm, trigonometry and some older video on ioT/Smart Home:
MIT Integration Bee
Area Under Curves
JEE-Main, India
UK AQA/CIE A-Level
Stanford Math Tournament
Calculus
[1] Solving Gaussian Integral (integration of gaussian function) by Feynman’s Method.
[2] Created another 1 minute video for Happy π day! Solve an integral and the answer is π!
[3] Solving integral x^(9)*(x^(10) + 1)/(x^(20) + 1) dx. Can we solve it using substitution?
[4] Solving integral 1/(-sqrt(x^2 + 4*x + 3)) dx. Can it be solved by substitution?
[5] Solving sum of k=0 to ∞ for integral sin^(2k) (x) dx. Solution is much easier than expected!
[6] Solving area of region bounded between 2 curves, i.e., {(x,y): x^2 ≤ y ≤ x + 2} using integration.
[7] Solving integral (x^2 - 1)/(x^4 - 1) dx.
[8] Given y=kx^2, x=ky^2, k is +ve constant & area enclosed between parabola curves is 1 unit^2. Find k.
[9] Given f(x) = integral (x^5-16x)/(x^8-256) dx and f(-2) = π/32. Find f(2). Explanation in 60 seconds
Algebra
[1] Is this a quartic or quadratic problem? Can we solve it within 60 seconds and without calculator?
[2] Solving (10016*104*12*8 + 256)^0.5 but without using calculator & computer. Answer is a nice number!
[4] 15 seconds video on solving sqrt(10300 - 9*10*10*11) without using calculator and computer.
[5] Given x^2 - x - 1 = 0, solve cos^1 ((3/2)*(7*x + 1)/(x^9 - 18*x - 13)).
[6] An infinite radical equation, i.e., sqrt(3*sqrt(7*sqrt(…))) solve by Geometric Series.
[7] If (√ 2 + √ 3)^11 = a √ 2 + b√ 3, then (a² - (3/2)*b²)^11 = ?
[8] Given (|x-3| - 4)^2 = 4. How many answers for x?
Logarithm/exponential
[1] Solving a finite power equation of (ln(x))^2. The solution is surprisingly easier than expected.
[2] Given that ln(3) is approximately equal to 1.099, find ln(3.1) using calculus without calculator.
[3] Solving x^(ln x) = x for real numbers. How many answers for x?
[4] Solving a radical-absolute equation. Is this a quadratic equation too?
[5] Solving a logarithm-quadratic question of Stanford Math Tournament 2021. Calculator is not allowed.
[6] 15 seconds video to explain the answer for ln(-1) based on principal value of trigonometry.
[7] 15 seconds video on solving x^(ln|x|) = 1/|x|. There are 4 answers for x?
Trigonometry
[1] Solving a trigonometry-power equation? Solution is fairly simple and can be explained in 60 seconds.
[2] 45 seconds video deriving cos(-θ)=cos(θ) & sin(-θ)=-sin(θ). Basic identities of trigonometry Part 5.
[3] 15 seconds video for deriving sec^2(x) = tan^2(x) + 1. Basic identities of trigonometry Part 1.
[4] 15 seconds video for deriving sin^2(x) + cos^2(x) = 1. Basic identities of trigonometry Part 2.
IoT/Smart Home
[1] Smart Home: Control Autogate using Sonoff RF Bridge with eWelink App & voice command of Amazon Alexa
[2] Can We Remote Access Node-red Server from another computer? Part 1: Wireless/Wire LAN
[3] How to install Amazon Alexa App on iPhone in Malaysia or region without it in Apple Store (Feb 2021)
[4] Smart Home: Security Automation Alarm System using Aqara G2H Camera Hub, Motion & Contact Sensors
[5] Node-red Iot Server & Telegram bot - Part 2: Search & display photo using telegrambot (Windows 10)
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