मराठी

Using L’Hospital Rule, Evaluate: Lim X → 0 8 X − 4 X 4 X - Mathematics

Advertisements
Advertisements

प्रश्न

Using L’Hospital Rule, evaluate: `lim_(x->0)  (8^x - 4^x)/(4x
)`

बेरीज

उत्तर

`lim_(x-.0) (8^x-4^x)`
`lim_(x->0)(8^xlog8 - 4^x log 4)`

`= (8^0 log 8 - 4^0 log 4)/4`
`=1/4log2`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2018-2019 (March) Set 1

APPEARS IN

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Evaluate `int_1^3(e^(2-3x)+x^2+1)dx`  as a limit of sum.


Evaluate the following definite integrals as limit of sums.

`int_0^5 (x+1) dx`


Evaluate the following definite integrals as limit of sums `int_(-1)^1 e^x dx`


Evaluate the definite integral:

`int_(pi/6)^(pi/3)  (sin x + cosx)/sqrt(sin 2x) dx`


Evaluate the definite integral:

`int_0^(pi/2) sin 2x tan^(-1) (sinx) dx`


Evaluate the definite integral:

`int_1^4 [|x - 1|+ |x - 2| + |x -3|]dx`


Prove the following:

`int_0^(pi/2) sin^3 xdx = 2/3`


Prove the following:

`int_0^1sin^(-1) xdx = pi/2 - 1`


`int dx/(e^x + e^(-x))` is equal to ______.


`int (cos 2x)/(sin x + cos x)^2dx` is equal to ______.


If f (a + b - x) = f (x), then `int_a^b x f(x )dx` is equal to ______.


` ∫  log x / x  dx `
 
 
 

\[\int\frac{1}{\sqrt{\tan^{- 1} x} . \left( 1 + x^2 \right)} dx\]

\[\int\frac{1}{x} \left( \log x \right)^2 dx\]


\[\int e^{cos^2 x}   \text{sin 2x  dx}\]

\[\int\frac{\sin x}{\left( 1 + \cos x \right)^2} dx\]

 


\[\text{ ∫  cosec x  log}      \left( \text{cosec x} - \cot x \right) dx\]

\[\int\frac{1}{x^2} \cos^2 \left( \frac{1}{x} \right) dx\]

\[\int\limits_{- \pi/2}^{\pi/2} \sin^4 x\ dx\]

Evaluate the following integrals as limit of sums:

\[\int_1^3 \left( 3 x^2 + 1 \right)dx\]

Evaluate `int_1^4 ( 1+ x +e^(2x)) dx` as limit of sums.


If f and g are continuous functions in [0, 1] satisfying f(x) = f(a – x) and g(x) + g(a – x) = a, then `int_0^"a" "f"(x) * "g"(x)"d"x` is equal to ______.


Evaluate the following as limit of sum:

`int_0^2 "e"^x "d"x`


Evaluate the following:

`int_0^pi x sin x cos^2x "d"x`


The value of `int_(-pi)^pi sin^3x cos^2x  "d"x` is ______.


The value of `lim_(x -> 0) [(d/(dx) int_0^(x^2) sec^2 xdx),(d/(dx) (x sin x))]` is equal to


What is the derivative of `f(x) = |x|` at `x` = 0?


`lim_(n→∞){(1 + 1/n^2)^(2/n^2)(1 + 2^2/n^2)^(4/n^2)(1 + 3^2/n^2)^(6/n^2) ...(1 + n^2/n^2)^((2n)/n^2)}` is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×