Determine the limit from a graph with a jump discontinuity, calculus 1 tutorial

Learn how to determine the limit from a graph with a jump discontinuity. Subscribe for more calculus 1 tutorials.

Evaluating Limits from a graph, jump discontinuity,
Limits from both sides,
Evaluating Limits from the definition of derivative,

----------------------------------------
#blackpenredpen #math #maths #trigonometry #calculus #tutorial

[jzanimates]

Now I see why the microphone is so important.

[legendarycosmo]

Could you do a video on some hard integration questions?
Would really prepare me for my Calculus 2 exams.

[turtlellamacow]

for question 6, you can just notice that it's the limit definition of the derivative of f(x) = 2x^2 - 5x, evaluated at x = 2: it's (f(2+h) - f(2))/h. of course it might be a little hard for high school students to deduce the form of that function and to notice that the +2 comes from subtracting f(2), so it's quicker to just expand it out. but it's good to keep in mind if they throw problems at you with the same structure but much high powers. and you could also l'hopital it, which is essentially the same process.

[rakhimondal]

2:21 Savage mode on...
Sure break-up!!!!

[roddy]

If you're familiar with derivatives you recognize Q6 as derivative:

f(x)=2x²-5x+C

f‘(2)=lim_h→0 of

f‘(2)=lim_h→0 of (2(2-h)²-5(2-h)+2)/h

f‘(x)=4x-5

f‘(2)=4(2)-5=8-5=3

[July-gjst]

Why not make a substitution for 2+h? It makes things way faster.

[el-mehdibenchaib]

I need some help with this :

Prove that 2*(cos (4*pi/19 )+ cos (6pi/19) + cos (10pi/19)) is a root of the equation:

sqrt(4 +sqrt(4 + sqrt(4 − x))) = x

[qingyangzhang]

OMG I am so proud of myself for factorising question six as a quadratic in disguise, and then solving the whole problem and getting the right answer with much more elegant algebra manipulation. I separated the -5(2+h) into a -4(2+h) and a -(2+h) and factorised the quadratic. Btw I am a high school student who has not yet started calculus in school, so this is not easy.

[jhrraz]

can you make more videos about hyporbolic functions limits and exponentials they're giving me a really hard time :'(

[maximilianludwig]

Why didn't you use the bro l'Hopital? XD

[yrret]

Why not just use lopital? So much quicker