Class 11 Exam > Class 11 Videos > Introduction to Calculus (Part - 1) - limits and derivatives, Mathematics, Class 11
Introduction to Calculus (Part - 1) - limits and derivatives, Mathematics, Class 11 Video Lecture
FAQs on Introduction to Calculus (Part - 1) - limits and derivatives, Mathematics, Class 11 Video Lecture
| 1. What is the concept of limits in calculus? |  |
Ans. In calculus, the concept of limits is used to determine the behavior of a function as it approaches a certain point. It helps us understand how the function behaves near that point without actually evaluating the function at that point. Limits are used to define the derivative and integral, which are fundamental concepts in calculus.
| 2. How do you find the limit of a function? | |
Ans. To find the limit of a function, you can evaluate the function at values approaching the given point and observe the pattern. If the function approaches a specific value as the input values get closer and closer to the given point, then that value is the limit of the function at that point. You can also use algebraic techniques, such as factoring or rationalizing, to simplify the function and then evaluate the limit.
| 3. What is the derivative of a function in calculus? | |
Ans. The derivative of a function measures how the function changes as its input changes. It represents the rate of change of the function at a specific point. Geometrically, it represents the slope of the tangent line to the graph of the function at that point. The derivative is a fundamental concept in calculus and has various applications in physics, engineering, and economics.
| 4. How do you find the derivative of a function? | |
Ans. To find the derivative of a function, you can use the rules of differentiation, such as the power rule, product rule, quotient rule, and chain rule. These rules provide a systematic way to find the derivative of different types of functions. You can also use the concept of limits to find the derivative by calculating the slope of the tangent line as the change in input approaches zero.
| 5. What is the significance of limits and derivatives in calculus? | |
Ans. Limits and derivatives are fundamental concepts in calculus that play a crucial role in understanding the behavior of functions. Limits help us analyze the behavior of functions near a specific point, allowing us to determine their continuity, existence of limits, and evaluate complicated functions. Derivatives, on the other hand, provide information about the rate of change of a function, helping us analyze motion, optimization, and other real-world applications. They also help us find the slope of a curve, determine concavity, and locate critical points. Overall, limits and derivatives are essential tools for understanding the fundamental principles of calculus and its wide-ranging applications.
Text Transcript from Video
hello friends this week even limits and
derivatives part month has got you by
exam fear not form no more fear from
exam in this video we will study
calculus in calculus will study limits
limits will study left hand limit right
hand limit algebra favorite limits of
rational number and Sandra Stier will
also study derivatives in derivatives
will study first principle graphical
interpretation latest and algebra
derivative let me introduce you calculus
calculus is nothing but branch of
mathematics that deals me study of
change in the value of function with
respect to the main change example when
I say Y is equal to FX this is a
function so here if you see Y is the
value and X is nothing but knowing
alright so when I means talking about dy
by DX that is change in Y with respect
to X there is change in value of the
function with respect to domain of the
function then such study is part of
calculus let me repeat definition once
again calculus is nothing but the branch
of study that means deals with study of
change of the value of function with
respect to domain change for example
when you say a function y is equal to FX
in this case the value of the function
is y and the domain is X so when I am
talking about dy by DX there is change
of Y with respect to X or change your
value of the function with respect to X
such study is called calc let me take
one example let's see this car is moving
right so if you see this car what we can
see that let suppose this t is equal to
zero this is time this is t is equal to
1 T is going to give T is equal to T and
T is wonderful so let us suppose there
are four intervals you have taken
divided this into four intervals and at
this point distance covered was this
suppose 0 at this point distance cover
let's suppose was to this is
fine distance perverse for this point
distance fervor 6 and this point
distance called was did we show once
again the car moves at T is equal to 0
distance cover is 0 T is equal to 3
discount to 6t spent before doesn't
rolls it because we are amazing distance
from here so from here to here this
point is 0 from here to this point is 2
P and Q is T from Q to R again is 2 so
total point P R is 2+2 4 so this is 4
again R to s is again 2 so P SS 6 + SN
it suppose T is again 2 to total essence
is 8 so this is the distance so we have
this relation where time is in this 0 to
0 1 2 3 4 and distance is 0 2 4 6 8 so
if you observe this crap what we say we
can say that we can write s is equal to
K into T some constant e just by
observation we have seen that s is equal
to 0 T is equal to 0 s is good 2 P is
equal to 1 s going to 4 T is equal to 2
this relation we have and if you observe
we can see that K is your nothing but 2
why because you can say it 2 is equal to
K into 1 s is equal to K into T so you
get K is equal to 1 2 similarly here
also if you put the value in this
equation 4 is equal to K into 2 so k is
equal to so you see if we found that K
is equal to D so the equation is of this
form that is s is equal to 2 into T this
is the equation we have for the scenario
what difference notice may have
integration and base for this scenario
we have this equation now if I want to
find the rate of change of s that is
distance with respect to time we'll call
it d s by DT that is rate of change of s
with respect to time here if you see S
is nothing but value and T is nothing
but doing so here once again we come for
definition
calculus is nothing but branch of
mathematics that deal with the study of
change of value with respect to study
with respect to change in domain if you
change in domain is one what should be
the change in value of s that that kind
of study is called calculus we'll
discuss more in detail but just remember
that calculus is nothing but branch of
mathematics that deals with study of
chilling in the value of function the
value of function with the main chain so
domain is here T and value of function
is s because our function is s is going
to routine atlas in the scenario to
insist nano for example we know we want
to find the speed of the car speed is
nothing but s parity or DS by DT so if
we know this value we can find out speed
so this calculus will help us to find
the speed of the car also you want to
find the speed of activation of the car
that can also be found the calculus so
calculus has varied implementation in
terms of physics astronomy in various
places we used calculus just you should
know that calculus is nothing but branch
of mathematics that deals with study or
change in value of function the value of
function there is d of value of function
by D of domain domain change because the
function is nothing but something is
written in domain so change in value or
function with respect to domain this is
thank you
visit exam viacom to watch free
education videos try free online tests
in the best quality study materials
study from the best tutors and mentors
and much more thanks again
derivatives part month has got you by
exam fear not form no more fear from
exam in this video we will study
calculus in calculus will study limits
limits will study left hand limit right
hand limit algebra favorite limits of
rational number and Sandra Stier will
also study derivatives in derivatives
will study first principle graphical
interpretation latest and algebra
derivative let me introduce you calculus
calculus is nothing but branch of
mathematics that deals me study of
change in the value of function with
respect to the main change example when
I say Y is equal to FX this is a
function so here if you see Y is the
value and X is nothing but knowing
alright so when I means talking about dy
by DX that is change in Y with respect
to X there is change in value of the
function with respect to domain of the
function then such study is part of
calculus let me repeat definition once
again calculus is nothing but the branch
of study that means deals with study of
change of the value of function with
respect to domain change for example
when you say a function y is equal to FX
in this case the value of the function
is y and the domain is X so when I am
talking about dy by DX there is change
of Y with respect to X or change your
value of the function with respect to X
such study is called calc let me take
one example let's see this car is moving
right so if you see this car what we can
see that let suppose this t is equal to
zero this is time this is t is equal to
1 T is going to give T is equal to T and
T is wonderful so let us suppose there
are four intervals you have taken
divided this into four intervals and at
this point distance covered was this
suppose 0 at this point distance cover
let's suppose was to this is
fine distance perverse for this point
distance fervor 6 and this point
distance called was did we show once
again the car moves at T is equal to 0
distance cover is 0 T is equal to 3
discount to 6t spent before doesn't
rolls it because we are amazing distance
from here so from here to here this
point is 0 from here to this point is 2
P and Q is T from Q to R again is 2 so
total point P R is 2+2 4 so this is 4
again R to s is again 2 so P SS 6 + SN
it suppose T is again 2 to total essence
is 8 so this is the distance so we have
this relation where time is in this 0 to
0 1 2 3 4 and distance is 0 2 4 6 8 so
if you observe this crap what we say we
can say that we can write s is equal to
K into T some constant e just by
observation we have seen that s is equal
to 0 T is equal to 0 s is good 2 P is
equal to 1 s going to 4 T is equal to 2
this relation we have and if you observe
we can see that K is your nothing but 2
why because you can say it 2 is equal to
K into 1 s is equal to K into T so you
get K is equal to 1 2 similarly here
also if you put the value in this
equation 4 is equal to K into 2 so k is
equal to so you see if we found that K
is equal to D so the equation is of this
form that is s is equal to 2 into T this
is the equation we have for the scenario
what difference notice may have
integration and base for this scenario
we have this equation now if I want to
find the rate of change of s that is
distance with respect to time we'll call
it d s by DT that is rate of change of s
with respect to time here if you see S
is nothing but value and T is nothing
but doing so here once again we come for
definition
calculus is nothing but branch of
mathematics that deal with the study of
change of value with respect to study
with respect to change in domain if you
change in domain is one what should be
the change in value of s that that kind
of study is called calculus we'll
discuss more in detail but just remember
that calculus is nothing but branch of
mathematics that deals with study of
chilling in the value of function the
value of function with the main chain so
domain is here T and value of function
is s because our function is s is going
to routine atlas in the scenario to
insist nano for example we know we want
to find the speed of the car speed is
nothing but s parity or DS by DT so if
we know this value we can find out speed
so this calculus will help us to find
the speed of the car also you want to
find the speed of activation of the car
that can also be found the calculus so
calculus has varied implementation in
terms of physics astronomy in various
places we used calculus just you should
know that calculus is nothing but branch
of mathematics that deals with study or
change in value of function the value of
function there is d of value of function
by D of domain domain change because the
function is nothing but something is
written in domain so change in value or
function with respect to domain this is
thank you
visit exam viacom to watch free
education videos try free online tests
in the best quality study materials
study from the best tutors and mentors
and much more thanks again
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Nov 13, 2024 Last updated |
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