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Applied Mathematics - ll : Limits | Chapter 01 | Lecture 10 Notes For Polytechnic.
Hey Everyone, I will Show you How to Evaluate Of Exponential & Logarithmic Functions Very Important Questions which is Lecture 10 Of applied mathematics 2 Chapter 01 Of Module 2 Differentiation Calculus.
It's Very Important Lecture For All My students So Watch Video on youtube video & Download your Notes through below given link .
Lecture 10 Topics :
1 ) Evaluation Of Exponential Function & Logarithmic Function Limits .
2 ) Most Important Questions Based On Limits Of Exponential & Logarithmic Functions.
Evaluation Of Exponential Function & Logarithmic Function Limits
Theorem :
1 ) Lim a^x -1 / x = loga
x→0
2 ) Lim e^x - 1 / x = 1
x→0
3 ) lim log ( 1+ x ) / x = 1
x→0
Properties Of Logarithmic Function
- Product property of logarithms
The product rule states that multiplication of two or more logarithms with common bases is equal to the adding the individual logarithms .
1. log ( PQ ) = Log (P ) + Log ( Q )
- Quotient property of logarithms
This rule states that the ratio of two logarithms with same bases is equal to the difference of the logarithms
2 ) Log ( P/Q ) = Log ( P) - Log ( Q )
- Power property of logarithms
According to the power property of logarithm, the log of a number ‘M’ with exponent ‘n’ is equal to the product of exponent with log of a number (without exponent)
3 ) log (x^n) = n log ( x )
- Change of base property of logarithms
According to the change of base property of logarithm, we can rewrite a given logarithm as the ratio of two logarithms with any new base.
4 ) log a M = log b M/ log b N
Important Question Based Exponential Function
Question 01
Evaluate : Lim ( 2^t - 1 )
t →0 t
Solution : View On This Page
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Question 01
|
Evaluate : Lim a^x - b^x
x→0 x
Solution : View On This Page
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| ( Question 02 ) |
Question 03 :
Evaluate : Lim 2^x - 1
x→0 ✓ 1+ x - 1
Solution : View On This Page
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| ( Question 03 ) |
Question 04 ;
Evaluate : Lim 2^3x - 3^ x
x →0 sin3x
Solution : View On This Page
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| ( Question 04 ) |
Question 05 :
Evaluate :
Lim 10^x - 2^x -5^x + 1
x→0 xsinx
Solution : View On This Page
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| ( Question 05 ) |
Question 06 ;
Evaluate : lim 3^x +3^-x - 2
x→0 x²
Solution : View On This Page
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| ( Question 06 ) |
Question 07;
Evaluate : Lim log ( 1+ x³ )
x→0 Sin³x
Solution : View On This Page
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| ( Question 07 ) |
Question 08 ;
Evaluate : Lim log x - 1
x →e x - e
Solution : View On This Page
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| ( Question 08 ) |
Question 09 ;
Write The Value Of :
lim e ^ 3sinx - 1
x→0 x
Solution : View On this Page
 |
| ( Question 09 ) |
Important Trigonometry Formula
- sin(x+y) = sin(x)cos(y)+cos(x)sin(y)
- cos(x+y) = cos(x)cos(y)–sin(x)sin(y)
- sin(x–y) = sin(x)cos(y)–cos(x)sin(y)
- cos(x–y) = cos(x)cos(y) + sin(x)sin(y)
And Also ,- SinA + SinB = 2sin (A + B )/2 Cos( A - B )/2
- SinA - SinB = 2Cos (A + B )/2 Sin( A - B )/2
- CosA + CosB = 2Cos(A + B )/2 Cos( A - B )/2
- CosA - CosB = - 2Sin (A + B )/2 Sin( A - B )/2
This Is complete Notes of Lecture 10 Of Chapter 01 Limits
Thank You For Visiting ✔️
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