Grade 12Differential Calculus
what is Lim x tends to 0 ( 1 +ax) to the power of 1/x ?
what is Lim x tends to 0 ( 1 +ax) to the power of 1/x ?
2 Answers
Nandana
it’s become 1
as lim x → 0 (1+a*0) = 1
& 1 ^ (infinite ) = 1
so the answer is ‘1’
this is also done by expanding of Binomial series, then also we get 1
by this way -
1+ 1/x(ax) /1! + 1/x(1/(x-1))/2! + …
as we seen that except 1st term all terms are multiplied by ‘x’, as x tending to ‘0’ these terms also =0
& we left with ‘1’ .
Nandana
sorry , it’s my mistake it’s not ‘1’ , it is e^a ,
lim x → 0 (1 +ax )^(1/x) is obtained by expansion of binomial series as follows –
=> (01/x)(1*(ax)^0) + (11/x)(ax)^1 + (21/x)(ax)^2 + …. (1/x1/x) (ax)^(1/x)
=> 1+ (a/1!)+(a^2/2!)+ (a^3/3!)+ …..
=> e^a [since e^x = 1+(x/1!)+(x^2/2!)+(x^3/3!)+ … ]
Other Related Questions on differential calculus
the diameter of a roller is 84 cm and its length is 120 cm. it takes 500 complete revolution to move once over to level a playground. find the area of the playground in square m?
the diameter of a roller is 84 cm and its length is 120 cm. it takes 500 complete revolution to move once over to level a playground. find the area of the playground in square m?
differential calculus
Last Activity: 3 Years ago
Find dy/DX when y=x^sinx+sin-1√x. Please give me the solution of this problem.
Find dy/DX when y=x^sinx+sin-1√x.
Please give me the solution of this problem.
differential calculus
Last Activity: 4 Years ago
If domain of f(x) is [-1, 2], then find the domain of f([x]-x^2+4), where [ ]denotes greatest integer function.
If domain of f(x) is [-1, 2], then find the domain of f([x]-x^2+4), where [ ]denotes greatest integer function.
differential calculus
Last Activity: 4 Years ago
Solve the differential equation y’’+2ty’-4y=1, y(0)=y’(0)=0.
Solve the differential equation y’’+2ty’-4y=1, y(0)=y’(0)=0.
differential calculus
Last Activity: 4 Years ago
Example 20. (i) In a AABC, find the maxima and minima of u = sin A sin B sin Cwhere A + B + C = T(ii) In a plane triangle ABC, find the maximum value of cosA cosB cosC.
Example 20. (i) In a AABC, find the maxima and minima of u = sin A sin B sin C
where A + B + C = T
(ii) In a plane triangle ABC, find the maximum value of cosA cosB cosC.
differential calculus
Last Activity: 4 Years ago